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Volumn 2, Issue , 2002, Pages 503-597

Chapter 11 Navier-Stokes equations and dynamical systems

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EID: 33748532060     PISSN: 1874575X     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S1874-575X(02)80032-7     Document Type: Chapter
Times cited : (7)

References (180)
  • 1
    • 67649408616 scopus 로고    scopus 로고
    • R. Abraham and J. Marsden, Foundation of Mechanics, Benjamin, Reading, MA
    • R. Abraham and J. Marsden, Foundation of Mechanics, Benjamin, Reading, MA.
  • 2
    • 0001709855 scopus 로고
    • Steady gas flows past bodies at small Knudsen numbers
    • Aoki K., and Sone Y. Steady gas flows past bodies at small Knudsen numbers. Transport Theory Statist. Phys. 16 (1987) 189-199
    • (1987) Transport Theory Statist. Phys. , vol.16 , pp. 189-199
    • Aoki, K.1    Sone, Y.2
  • 3
    • 0003356898 scopus 로고    scopus 로고
    • Topological Methods in Hydrodynamics
    • Springer, Berlin
    • Arnold V.I., and Khesin B.A. Topological Methods in Hydrodynamics. Appl. Math. Sci. Vol. 125 (1998), Springer, Berlin
    • (1998) Appl. Math. Sci. , vol.125
    • Arnold, V.I.1    Khesin, B.A.2
  • 5
    • 0039721779 scopus 로고    scopus 로고
    • On the regularity of three-dimensional rotating Navier-Stokes equations
    • Avrin J., Babin A., Mahalov A., and Nicolaenko B. On the regularity of three-dimensional rotating Navier-Stokes equations. Appl. Anal. 71 (1999) 197-214
    • (1999) Appl. Anal. , vol.71 , pp. 197-214
    • Avrin, J.1    Babin, A.2    Mahalov, A.3    Nicolaenko, B.4
  • 6
    • 0000190618 scopus 로고    scopus 로고
    • Global regularity and integrability of 3D Euler and Navier-Stokes equations for uniformly rotating fluids
    • Babin A., Mahalov A., and Nicolaenko B. Global regularity and integrability of 3D Euler and Navier-Stokes equations for uniformly rotating fluids. Asymptotic Anal. 15 2 (1997) 103-150
    • (1997) Asymptotic Anal. , vol.15 , Issue.2 , pp. 103-150
    • Babin, A.1    Mahalov, A.2    Nicolaenko, B.3
  • 7
    • 0012375854 scopus 로고    scopus 로고
    • Fast singular oscillating limits of stably stratified three-dimensional Euler-Boussinesq equations and ageostrophic wave fronts
    • Cambridge Univ. Press, Cambridge to appear
    • A. Babin, A. Mahalov and B. Nicolaenko, Fast singular oscillating limits of stably stratified three-dimensional Euler-Boussinesq equations and ageostrophic wave fronts, Newton Institute of Mathematical Sciences Series, Cambridge Univ. Press, Cambridge (to appear).
    • Newton Institute of Mathematical Sciences Series
    • Babin, A.1    Mahalov, A.2    Nicolaenko, B.3
  • 8
    • 0010831910 scopus 로고
    • Long-time averaged Euler and Navier-Stokes equations for rotating fluids
    • Kirchgässner K., and Mielke A. (Eds), World Scientific, Singapore
    • Babin A., Mahalov A., and Nicolaenko B. Long-time averaged Euler and Navier-Stokes equations for rotating fluids. In: Kirchgässner K., and Mielke A. (Eds). Structure and Dynamics of Nonlinear Waves in Fluids (1995), World Scientific, Singapore 145-157
    • (1995) Structure and Dynamics of Nonlinear Waves in Fluids , pp. 145-157
    • Babin, A.1    Mahalov, A.2    Nicolaenko, B.3
  • 9
    • 0030313282 scopus 로고    scopus 로고
    • Resonances and regularity for Boussinesq equations
    • Babin A., Mahalov A., and Nicolaenko B. Resonances and regularity for Boussinesq equations. Russian J. Math. Phys. 4 4 (1996) 417-428
    • (1996) Russian J. Math. Phys. , vol.4 , Issue.4 , pp. 417-428
    • Babin, A.1    Mahalov, A.2    Nicolaenko, B.3
  • 10
    • 0029695832 scopus 로고    scopus 로고
    • Global splitting integrability and regularity of 3D Euler and Navier-Stokes equations for uniformly rotating fluids
    • Babin A., Mahalov A., and Nicolaenko B. Global splitting integrability and regularity of 3D Euler and Navier-Stokes equations for uniformly rotating fluids. Europ. J. Mechanics B/Fluids 15 3 (1996) 291-300
    • (1996) Europ. J. Mechanics B/Fluids , vol.15 , Issue.3 , pp. 291-300
    • Babin, A.1    Mahalov, A.2    Nicolaenko, B.3
  • 11
    • 0038449701 scopus 로고    scopus 로고
    • Global regularity of the 3D rotating Navier-Stokes equation for resonant domains
    • Babin A., Mahalov A., and Nicolaenko B. Global regularity of the 3D rotating Navier-Stokes equation for resonant domains. Indiana Univ. Math. J. 48 3 (1999) 1133-1176
    • (1999) Indiana Univ. Math. J. , vol.48 , Issue.3 , pp. 1133-1176
    • Babin, A.1    Mahalov, A.2    Nicolaenko, B.3
  • 12
    • 0034383815 scopus 로고    scopus 로고
    • Nicolaenko, On the regularity of three-dimensional rotating Euler-Bous-sinesq equations
    • Babin A., Mahalov A., and Nicolaenko B. Nicolaenko, On the regularity of three-dimensional rotating Euler-Bous-sinesq equations. MMNS 34 2 (2000) 201-222
    • (2000) MMNS , vol.34 , Issue.2 , pp. 201-222
    • Babin, A.1    Mahalov, A.2    Nicolaenko, B.3
  • 13
    • 0012408816 scopus 로고    scopus 로고
    • 3D Navier-Stokes and Euler equations with initial data characterized by uniformly large vorticity
    • in press
    • in press. Babin A., Mahalov A., and Nicolaenko B. 3D Navier-Stokes and Euler equations with initial data characterized by uniformly large vorticity. Indiana Univ. Math. J. (2001)
    • (2001) Indiana Univ. Math. J.
    • Babin, A.1    Mahalov, A.2    Nicolaenko, B.3
  • 14
    • 0003014302 scopus 로고
    • Attractors of partial differential equations and estimates of their dimension
    • in Russian
    • in Russian. Babin A.V., and Vishik M.I. Attractors of partial differential equations and estimates of their dimension. Uspekhi Mat. Nauk 38 (1983) 133-187
    • (1983) Uspekhi Mat. Nauk , vol.38 , pp. 133-187
    • Babin, A.V.1    Vishik, M.I.2
  • 16
    • 0001753772 scopus 로고
    • Regular attractors of semigroups and evolution equations
    • Babin A.V., and Vishik M.I. Regular attractors of semigroups and evolution equations. J. Math. Pures Appl. 62 (1983) 441-491
    • (1983) J. Math. Pures Appl. , vol.62 , pp. 441-491
    • Babin, A.V.1    Vishik, M.I.2
  • 17
    • 0042887224 scopus 로고
    • Maximal attractors of semigroups corresponding to evolution differential equations
    • in Russian
    • in Russian. Babin A.V., and Vishik M.I. Maximal attractors of semigroups corresponding to evolution differential equations. Mat. Sb. 126 (1985) 168
    • (1985) Mat. Sb. , vol.126 , pp. 168
    • Babin, A.V.1    Vishik, M.I.2
  • 18
    • 67649394024 scopus 로고
    • Math. USSR-Sb. 54 (1986) 387-408
    • (1986) Math. USSR-Sb. , vol.54 , pp. 387-408
  • 19
    • 0004227819 scopus 로고
    • (in Russian), North-Holland, Amsterdam (1992) (in English), Nauka, Moscow
    • (in Russian), North-Holland, Amsterdam (1992) (in English). Babin A.V., and Vishik M.I. Attractors of Evolution Equations (1989), Nauka, Moscow
    • (1989) Attractors of Evolution Equations
    • Babin, A.V.1    Vishik, M.I.2
  • 20
    • 21844481531 scopus 로고
    • Equations de transport relatives à des champs de vecteurs non-lipschitziens et mécanique des fluides
    • Bahouri H., and Chemin J.Y. Equations de transport relatives à des champs de vecteurs non-lipschitziens et mécanique des fluides. Arch. Rat. Mech. Anal. 127 (1994) 159-182
    • (1994) Arch. Rat. Mech. Anal. , vol.127 , pp. 159-182
    • Bahouri, H.1    Chemin, J.Y.2
  • 21
    • 0001101971 scopus 로고
    • Sur les limites asymptotiques de la théorie cinétique conduisant à la dynamique des fluides incompressibles
    • Bardos C., Golse F., and Levermore D. Sur les limites asymptotiques de la théorie cinétique conduisant à la dynamique des fluides incompressibles. C. R. Acad. Sci. 309 (1989) 727-732
    • (1989) C. R. Acad. Sci. , vol.309 , pp. 727-732
    • Bardos, C.1    Golse, F.2    Levermore, D.3
  • 22
    • 0001076950 scopus 로고
    • Fluid dynamics limits of kinetic equations I: Formal derivations
    • Bardos C., Golse F., and Levermore D. Fluid dynamics limits of kinetic equations I: Formal derivations. J. Statist. Phys. 63 (1991) 323-344
    • (1991) J. Statist. Phys. , vol.63 , pp. 323-344
    • Bardos, C.1    Golse, F.2    Levermore, D.3
  • 23
    • 84990619144 scopus 로고
    • Fluid dynamics limits of kinetic equations II: Convergence proofs for the Boltzmann equation
    • Bardos C., Golse F., and Levermore D. Fluid dynamics limits of kinetic equations II: Convergence proofs for the Boltzmann equation. Comm. Pure Appl. Math. 46 (1993) 667-753
    • (1993) Comm. Pure Appl. Math. , vol.46 , pp. 667-753
    • Bardos, C.1    Golse, F.2    Levermore, D.3
  • 27
    • 0001315807 scopus 로고
    • The Classical incompressible Navier-Stokes limit of the Boltzmann equation
    • Bardos C., and Ukai S. The Classical incompressible Navier-Stokes limit of the Boltzmann equation. Math. Models Methods Appl. Sci. 1 (1991) 235-257
    • (1991) Math. Models Methods Appl. Sci. , vol.1 , pp. 235-257
    • Bardos, C.1    Ukai, S.2
  • 28
    • 34250136481 scopus 로고
    • Remarks on the breakdown of smoothness for the 3-D Euler equations
    • Beale J., Kato T., and Majda A. Remarks on the breakdown of smoothness for the 3-D Euler equations. Comm. Math. Phys. 152 (1993) 61-66
    • (1993) Comm. Math. Phys. , vol.152 , pp. 61-66
    • Beale, J.1    Kato, T.2    Majda, A.3
  • 30
    • 84869291389 scopus 로고    scopus 로고
    • Limite des équations d'un fluide compressible lorsquela compressibilité tend vers zéro
    • H.B. Da Veiga, ed
    • A. Benabdallah-Lagha, Limite des équations d'un fluide compressible lorsquela compressibilité tend vers zéro, H.B. Da Veiga, ed., Springer Lecture Notes, Vol. 1047.
    • Springer Lecture Notes , vol.1047
    • Benabdallah-Lagha, A.1
  • 33
    • 67649397177 scopus 로고    scopus 로고
    • D.C. Besnard, F.H. Harlow, R.M. Rauenzahn and C. Zemach, Spectral transport model for turbulence, Los Alamos Technical Report LA-11821-MS.
    • D.C. Besnard, F.H. Harlow, R.M. Rauenzahn and C. Zemach, Spectral transport model for turbulence, Los Alamos Technical Report LA-11821-MS.
  • 34
    • 49149142420 scopus 로고
    • Nonlinear Schrödinger evolution equations
    • Brezis H., and Gallouet T. Nonlinear Schrödinger evolution equations. Nonlinear Anal. TMA 4 (1980) 677-681
    • (1980) Nonlinear Anal. TMA , vol.4 , pp. 677-681
    • Brezis, H.1    Gallouet, T.2
  • 35
    • 84990576577 scopus 로고
    • On the regularity of the solutions of the Navier-Stokes equa-tions
    • Caffarelli L., Kohn R.V., and Nirenberg L. On the regularity of the solutions of the Navier-Stokes equa-tions. Comm. Pure Appl. Math. 35 (1982) 771-831
    • (1982) Comm. Pure Appl. Math. , vol.35 , pp. 771-831
    • Caffarelli, L.1    Kohn, R.V.2    Nirenberg, L.3
  • 36
    • 34250258536 scopus 로고
    • The Boltzmann equation with a soft potential. I Linear spatially-homogeneous
    • Caflisch R. The Boltzmann equation with a soft potential. I Linear spatially-homogeneous. Comm. Math. Phys. 74 1 (1980) 71-95
    • (1980) Comm. Math. Phys. , vol.74 , Issue.1 , pp. 71-95
    • Caflisch, R.1
  • 37
    • 84980175331 scopus 로고
    • The fluid dynamic limit of the Boltzmann equation
    • Caflisch R. The fluid dynamic limit of the Boltzmann equation. Comm. Pure Appl. Math. 33 (1980) 651-666
    • (1980) Comm. Pure Appl. Math. , vol.33 , pp. 651-666
    • Caflisch, R.1
  • 38
    • 0040156965 scopus 로고
    • Asymptotic expansions of solutions for the Boltzmann equation
    • Proceedings of the Conference on Mathematical Methods Applied to Kinetic Equations. Paris 1985 4-6
    • Caflisch R. Asymptotic expansions of solutions for the Boltzmann equation. Proceedings of the Conference on Mathematical Methods Applied to Kinetic Equations. Paris 1985. Transport Theory Statist. Phys. 16 (1987) 701-725 4-6
    • (1987) Transport Theory Statist. Phys. , vol.16 , pp. 701-725
    • Caflisch, R.1
  • 39
    • 0031116236 scopus 로고    scopus 로고
    • Navier-Stokes equations on a circular domain construction of the solution and zero viscosity limit
    • Caflisch R., and Sammartino M. Navier-Stokes equations on a circular domain construction of the solution and zero viscosity limit. C. R. Acad. Sci. Sér. I 324 (1997) 861-866
    • (1997) C. R. Acad. Sci. Sér. I , vol.324 , pp. 861-866
    • Caflisch, R.1    Sammartino, M.2
  • 40
    • 0001296888 scopus 로고
    • A special class of stationary flows for two dimen-sional Euler equation: A statistical mechanics description
    • Caglioti E., Lions PL., Marchioro C., and Pulvirenti M. A special class of stationary flows for two dimen-sional Euler equation: A statistical mechanics description. Comm. Math. Phys. 143 (1992) 501-525
    • (1992) Comm. Math. Phys. , vol.143 , pp. 501-525
    • Caglioti, E.1    Lions, PL.2    Marchioro, C.3    Pulvirenti, M.4
  • 41
    • 0012523604 scopus 로고
    • A special class of stationary flows for two di-mensional Euler equation: A statistical mechanics description, Part II
    • Caglioti E., Lions P.L., Marchioro C., and Pulvirenti M. A special class of stationary flows for two di-mensional Euler equation: A statistical mechanics description, Part II. Comm. Math. Phys. 174 (1995) 229-260
    • (1995) Comm. Math. Phys. , vol.174 , pp. 229-260
    • Caglioti, E.1    Lions, P.L.2    Marchioro, C.3    Pulvirenti, M.4
  • 45
    • 0003200990 scopus 로고
    • The Mathematical Theory of Dilute Gases
    • Springer, New York
    • Cercignani C., Illner R., and Pulvirenti M. The Mathematical Theory of Dilute Gases. Appl. Math. Sci. Vol. 106 (1994), Springer, New York
    • (1994) Appl. Math. Sci. , vol.106
    • Cercignani, C.1    Illner, R.2    Pulvirenti, M.3
  • 46
    • 38249013140 scopus 로고
    • On the ensemble average in the study of approximate inertial manifolds II
    • Chae D. On the ensemble average in the study of approximate inertial manifolds II. J. Math. Anal. Appl. 614 (1992) 337-349
    • (1992) J. Math. Anal. Appl. , vol.614 , pp. 337-349
    • Chae, D.1
  • 48
    • 0003360134 scopus 로고
    • The Couette-Taylor Problem
    • Springer, Berlin
    • Chossat P., and Iooss G. The Couette-Taylor Problem. Appl. Math. Sci. Vol. 102 (1994), Springer, Berlin
    • (1994) Appl. Math. Sci. , vol.102
    • Chossat, P.1    Iooss, G.2
  • 49
    • 0013093539 scopus 로고
    • Vorticity and Turbulence
    • Springer, Berlin
    • Chorin A.J. Vorticity and Turbulence. Appl. Math. Sci. Vol. 103 (1994), Springer, Berlin
    • (1994) Appl. Math. Sci. , vol.103
    • Chorin, A.J.1
  • 50
    • 0242330113 scopus 로고
    • ∞ estimates for family of functions with orthonormal derivatives
    • ∞ estimates for family of functions with orthonormal derivatives. Indiana Univ. Math. J. 36 (1987) 603-616
    • (1987) Indiana Univ. Math. J. , vol.36 , pp. 603-616
    • Constantin, P.1
  • 51
    • 0028388187 scopus 로고
    • Geometric statistics in turbulence
    • Constantin P. Geometric statistics in turbulence. SIAM Rev. 361 (1994) 73-98
    • (1994) SIAM Rev. , vol.361 , pp. 73-98
    • Constantin, P.1
  • 52
    • 0030359563 scopus 로고    scopus 로고
    • Rigourous estimates of small scales in turbulent flows
    • Constantin P., Doering C., and Titi E.S. Rigourous estimates of small scales in turbulent flows. J. Math. Phys. 37 12 (1996) 6152-6156
    • (1996) J. Math. Phys. , vol.37 , Issue.12 , pp. 6152-6156
    • Constantin, P.1    Doering, C.2    Titi, E.S.3
  • 53
    • 0000646280 scopus 로고
    • Direction ofvorticity and the problem of global regularity for the Navier-Stokes Equations
    • Constantin P., and Fefferman C. Direction ofvorticity and the problem of global regularity for the Navier-Stokes Equations. Indiana Univ. Math. J. 42 3 (1993) 775-789
    • (1993) Indiana Univ. Math. J. , vol.42 , Issue.3 , pp. 775-789
    • Constantin, P.1    Fefferman, C.2
  • 54
    • 85080852500 scopus 로고
    • Geometric constraints on potentially singular solutions for the Euler equations
    • Constantin P., Fefferman C., and Majda A. Geometric constraints on potentially singular solutions for the Euler equations. Comm. Partial Differential Equations 3 4 (1993) 559-571
    • (1993) Comm. Partial Differential Equations , vol.3 , Issue.4 , pp. 559-571
    • Constantin, P.1    Fefferman, C.2    Majda, A.3
  • 55
    • 84990581938 scopus 로고
    • Global Lyapunov exponents, Kaplan-Yorke^formulas and the dimension of the attractors for 2D Navier-Stokes equations
    • Constantin P., and Foias C. Global Lyapunov exponents, Kaplan-Yorke^formulas and the dimension of the attractors for 2D Navier-Stokes equations. Comm. Pure Appl. Math. 38 (1985) 1-27
    • (1985) Comm. Pure Appl. Math. , vol.38 , pp. 1-27
    • Constantin, P.1    Foias, C.2
  • 57
    • 0000073888 scopus 로고
    • Effects of the forcing function spectrum on the energy spectrum in 2-D turbulence
    • Constantin P., Foias C., and Manley O.P. Effects of the forcing function spectrum on the energy spectrum in 2-D turbulence. Phys. Fluids 6 (1994) 427-429
    • (1994) Phys. Fluids , vol.6 , pp. 427-429
    • Constantin, P.1    Foias, C.2    Manley, O.P.3
  • 58
    • 0021150102 scopus 로고
    • Determining modes and fractal dimension of turbulent flows
    • Constantin P., Foias C., Manley O.P., and Temam R. Determining modes and fractal dimension of turbulent flows. J. Fluid Mech. 150 (1985) 427-440
    • (1985) J. Fluid Mech. , vol.150 , pp. 427-440
    • Constantin, P.1    Foias, C.2    Manley, O.P.3    Temam, R.4
  • 59
    • 0003983878 scopus 로고
    • Integral and Inertial Manifolds for Dissipative Partial Differential Equations
    • Springer, New York
    • Constantin P., Foias C., Nicolaenko B., and Temam R. Integral and Inertial Manifolds for Dissipative Partial Differential Equations. Appl. Math. Sci. Vol. 70 (1989), Springer, New York
    • (1989) Appl. Math. Sci. , vol.70
    • Constantin, P.1    Foias, C.2    Nicolaenko, B.3    Temam, R.4
  • 61
    • 0023999086 scopus 로고
    • On the dimension of the attractor in two-dimensional turbulence
    • Constantin P., Foias C., and Temam R. On the dimension of the attractor in two-dimensional turbulence. Phys. D 30 (1988) 284-296
    • (1988) Phys. D , vol.30 , pp. 284-296
    • Constantin, P.1    Foias, C.2    Temam, R.3
  • 62
    • 0000997393 scopus 로고
    • The entropy admissibility criteria for solutions of hyperbolic conservation laws
    • Dafermos C. The entropy admissibility criteria for solutions of hyperbolic conservation laws. J. Differen-tial Equations 14 (1973) 202-212
    • (1973) J. Differen-tial Equations , vol.14 , pp. 202-212
    • Dafermos, C.1
  • 63
    • 84990591606 scopus 로고
    • Incompressible Navier-Stokes and Euler limits of the Boltzmann equation
    • DeMasi A., Esposito R., and Lebowitz J. Incompressible Navier-Stokes and Euler limits of the Boltzmann equation. Comm. Pure Appl. Math. 42 (1990) 1189-1214
    • (1990) Comm. Pure Appl. Math. , vol.42 , pp. 1189-1214
    • DeMasi, A.1    Esposito, R.2    Lebowitz, J.3
  • 64
    • 0000408106 scopus 로고
    • Uniqueness of solutions to hyperbolic conservations laws
    • DiPerna R. Uniqueness of solutions to hyperbolic conservations laws. Indiana Univ. Math. J. 28 (1979) 244-257
    • (1979) Indiana Univ. Math. J. , vol.28 , pp. 244-257
    • DiPerna, R.1
  • 65
    • 0001089576 scopus 로고
    • On the Cauchy problem for the Boltzmann equation: Global existence and weak stability results
    • DiPerna R., and Lions P.-L. On the Cauchy problem for the Boltzmann equation: Global existence and weak stability results. Ann. of Math. 130 (1990) 321-366
    • (1990) Ann. of Math. , vol.130 , pp. 321-366
    • DiPerna, R.1    Lions, P.-L.2
  • 66
  • 68
    • 0345985245 scopus 로고
    • Exponential attractors and their relevance to fluid dynamic systems
    • Eden A., Foias C., Nicolaenko B., and She Z.S. Exponential attractors and their relevance to fluid dynamic systems. Phys. D 63 (1993) 350-360
    • (1993) Phys. D , vol.63 , pp. 350-360
    • Eden, A.1    Foias, C.2    Nicolaenko, B.3    She, Z.S.4
  • 69
    • 0003240970 scopus 로고
    • Exponential Attractors for Dissipative Evolution Equations
    • Masson, Paris, Wiley, New York
    • Masson, Paris. Eden A., Foias C., Nicolaenko B., and Temam R. Exponential Attractors for Dissipative Evolution Equations. RAM Vol. 37 (1994), Wiley, New York
    • (1994) RAM , vol.37
    • Eden, A.1    Foias, C.2    Nicolaenko, B.3    Temam, R.4
  • 71
    • 0000664820 scopus 로고
    • Wavelet analysis of coherent structure in two dimensional turbulent flows
    • Moffat H.K., and Tsinober A. (Eds), Cambridge Univ. Press, Cambridge
    • Farge M., Colonna J.F., and Holschneider M. Wavelet analysis of coherent structure in two dimensional turbulent flows. In: Moffat H.K., and Tsinober A. (Eds). Topological Fluid Mech. (1990), Cambridge Univ. Press, Cambridge 765
    • (1990) Topological Fluid Mech. , pp. 765
    • Farge, M.1    Colonna, J.F.2    Holschneider, M.3
  • 72
    • 0027007487 scopus 로고
    • Improve predictability of Wavelet analysis of two dimensional turbulent flows using wavelet packet compression
    • Farge M., Goirand E., Meyer Y., Pascal F., and Wickerhauser M.V. Improve predictability of Wavelet analysis of two dimensional turbulent flows using wavelet packet compression. Fluid Dynamic Res. 10 (1992) 229-250
    • (1992) Fluid Dynamic Res. , vol.10 , pp. 229-250
    • Farge, M.1    Goirand, E.2    Meyer, Y.3    Pascal, F.4    Wickerhauser, M.V.5
  • 73
    • 5944246388 scopus 로고    scopus 로고
    • Non-Gaussianity and coherent vortex simulation for two dimen-sional turbulence using an adaptative orthogonal wavelet basis
    • Farge M., Schneider K., and Kevlahan N. Non-Gaussianity and coherent vortex simulation for two dimen-sional turbulence using an adaptative orthogonal wavelet basis. Phys. Fluids 11 (1999) 2187-2201
    • (1999) Phys. Fluids , vol.11 , pp. 2187-2201
    • Farge, M.1    Schneider, K.2    Kevlahan, N.3
  • 74
    • 0000358588 scopus 로고
    • Statistical study of the Navier-Stokes equations I
    • Foias C. Statistical study of the Navier-Stokes equations I. Rend. Sem. Mat. Univ. Padova 48 (1973) 219-348
    • (1973) Rend. Sem. Mat. Univ. Padova , vol.48 , pp. 219-348
    • Foias, C.1
  • 75
    • 0002187572 scopus 로고
    • Statistical study of the Navier-Stokes equations II
    • Foias C. Statistical study of the Navier-Stokes equations II. Rend. Sem. Mat. Univ. Padova 49 (1973) 9-123
    • (1973) Rend. Sem. Mat. Univ. Padova , vol.49 , pp. 9-123
    • Foias, C.1
  • 76
    • 0001300072 scopus 로고    scopus 로고
    • What do the Navier-Stokes equations tell us about turbulence?
    • Amer. Math. Soc, Providence, RI
    • Foias C. What do the Navier-Stokes equations tell us about turbulence?. Contemp. Math. Vol. 208 (1997), Amer. Math. Soc, Providence, RI 151-180
    • (1997) Contemp. Math. , vol.208 , pp. 151-180
    • Foias, C.1
  • 78
    • 0020830393 scopus 로고
    • On the stationary statistical solutions of the Navier-Stokes equa-tions
    • Foias C., Manley O.P., and Temam R. On the stationary statistical solutions of the Navier-Stokes equa-tions. Phys. D 9 (1983) 157-183
    • (1983) Phys. D , vol.9 , pp. 157-183
    • Foias, C.1    Manley, O.P.2    Temam, R.3
  • 79
    • 0000438691 scopus 로고
    • Bounds for the mean dissipation of 2-D enstropy and 3-D energy in turbulent flows
    • Foias C., Manley O.P., and Temam R. Bounds for the mean dissipation of 2-D enstropy and 3-D energy in turbulent flows. Phys. Lett. A 174 (1993) 210-215
    • (1993) Phys. Lett. A , vol.174 , pp. 210-215
    • Foias, C.1    Manley, O.P.2    Temam, R.3
  • 80
    • 0020830393 scopus 로고
    • Asymptotic analysis of the Navier-Stokes equations
    • Foias C., Manley O.P., Temam R., and Treves Y. Asymptotic analysis of the Navier-Stokes equations. Phys. D 9 (1983) 157-188
    • (1983) Phys. D , vol.9 , pp. 157-188
    • Foias, C.1    Manley, O.P.2    Temam, R.3    Treves, Y.4
  • 81
    • 0001047390 scopus 로고
    • Inertial manifolds for the Kuramoto-Sivashinsky equa-tion and an estimate of their lowest dimension
    • Foias C., Nicolaenko B., Sell G.R., and Temam R. Inertial manifolds for the Kuramoto-Sivashinsky equa-tion and an estimate of their lowest dimension. J. Math. Pures Appl. 67 (1988) 197-226
    • (1988) J. Math. Pures Appl. , vol.67 , pp. 197-226
    • Foias, C.1    Nicolaenko, B.2    Sell, G.R.3    Temam, R.4
  • 82
    • 0003169927 scopus 로고    scopus 로고
    • Finite fractal dimension and Hölder-Lipschitz parametrization
    • Foias C., and Olson E. Finite fractal dimension and Hölder-Lipschitz parametrization. Indiana Univ. Math. J. 45 3 (1996) 603-616
    • (1996) Indiana Univ. Math. J. , vol.45 , Issue.3 , pp. 603-616
    • Foias, C.1    Olson, E.2
  • 83
    • 67649401569 scopus 로고
    • Sur les solutions statistiques des equations de Navier-Stokes
    • Foias C., and Prodi G. Sur les solutions statistiques des equations de Navier-Stokes. Ann. Math. Pura Appl. 4 (1973) 107-330
    • (1973) Ann. Math. Pura Appl. , vol.4 , pp. 107-330
    • Foias, C.1    Prodi, G.2
  • 84
    • 0000640733 scopus 로고
    • Inertial manifolds for nonlinear evolution equations
    • Foias C., Sell G., and Temam R. Inertial manifolds for nonlinear evolution equations. J. Differential Equa-tions 73 (1988) 309-353
    • (1988) J. Differential Equa-tions , vol.73 , pp. 309-353
    • Foias, C.1    Sell, G.2    Temam, R.3
  • 85
    • 0039044573 scopus 로고
    • Homogeneous statistical solutions of the Navier-Stokes
    • Foias C., and Temam R. Homogeneous statistical solutions of the Navier-Stokes. Indiana Univ. Math. J. 29 (1980) 913-957
    • (1980) Indiana Univ. Math. J. , vol.29 , pp. 913-957
    • Foias, C.1    Temam, R.2
  • 86
    • 0000263117 scopus 로고
    • Some analytic and geometric properties of the solutions of the evolution Navier-Stokes equations
    • Foias C., and Temam R. Some analytic and geometric properties of the solutions of the evolution Navier-Stokes equations. J. Math. Pures Appl. 58 (1979) 339-368
    • (1979) J. Math. Pures Appl. , vol.58 , pp. 339-368
    • Foias, C.1    Temam, R.2
  • 87
    • 33746636159 scopus 로고
    • Gevrey class regularity for the solutions of the Navier-Stokes equations
    • Foias C., and Temam R. Gevrey class regularity for the solutions of the Navier-Stokes equations. J. Funct. Anal. 87 (1989) 359-369
    • (1989) J. Funct. Anal. , vol.87 , pp. 359-369
    • Foias, C.1    Temam, R.2
  • 88
    • 67649401570 scopus 로고
    • The rate of convergence for the closure of the Friedman-Keller chain in the case of large Reynolds numbers
    • Fursikov A., and Ehmanuilov O. The rate of convergence for the closure of the Friedman-Keller chain in the case of large Reynolds numbers. Russ. Acad. Sci. Sb. Mat. 81 (1995) 235-259
    • (1995) Russ. Acad. Sci. Sb. Mat. , vol.81 , pp. 235-259
    • Fursikov, A.1    Ehmanuilov, O.2
  • 90
    • 0004185784 scopus 로고
    • Cambridge Univ. Press, Cambridge
    • Frisch U. Turbulence (1995), Cambridge Univ. Press, Cambridge
    • (1995) Turbulence
    • Frisch, U.1
  • 91
    • 0001250839 scopus 로고
    • A simple dynamical model of intermittent fully developed turbulence
    • Frisch U., Nelkin M., and Sulem P.-L. A simple dynamical model of intermittent fully developed turbulence. J. Fluid Mech. 87 (1978) 719-736
    • (1978) J. Fluid Mech. , vol.87 , pp. 719-736
    • Frisch, U.1    Nelkin, M.2    Sulem, P.-L.3
  • 93
    • 33646525656 scopus 로고    scopus 로고
    • From Kinetic to Macroscopic Models
    • to appear. Session "L'Etat de la Recherche" de la Soc. Math. de France, Orléans, Juin, Gauthier-Villars, Editions Scientifiques et Médicales Elsevier, Paris
    • to appear. Golse F. From Kinetic to Macroscopic Models. Session "L'Etat de la Recherche" de la Soc. Math. de France, Orléans, Juin. Series in Applied Mathematics (1998), Gauthier-Villars, Editions Scientifiques et Médicales Elsevier, Paris
    • (1998) Series in Applied Mathematics
    • Golse, F.1
  • 94
    • 16744364213 scopus 로고    scopus 로고
    • The Navier-Stokes limit for the Boltzmann equation
    • to appear
    • to appear. Golse F., and Raymond L.S. The Navier-Stokes limit for the Boltzmann equation. C. R. Acad. Sci. Paris Sér. 1332 (2001)
    • (2001) C. R. Acad. Sci. Paris Sér. , vol.1332
    • Golse, F.1    Raymond, L.S.2
  • 95
    • 0002040149 scopus 로고
    • Solutions in the large for nonlinear systems of conservation laws
    • Glimm J. Solutions in the large for nonlinear systems of conservation laws. Comm. Pure Appl. Math. 18 (1965) 685-715
    • (1965) Comm. Pure Appl. Math. , vol.18 , pp. 685-715
    • Glimm, J.1
  • 96
    • 0001294845 scopus 로고
    • Principles of the kinetic theory of gases
    • Thermodynamik der Gase, Springer, Berlin
    • Grad H. Principles of the kinetic theory of gases. Thermodynamik der Gase. Handbuch der Physic Bd. 12 (1958), Springer, Berlin 205-294
    • (1958) Handbuch der Physic , vol.Bd. 12 , pp. 205-294
    • Grad, H.1
  • 97
    • 0001467016 scopus 로고
    • Global validity of the Boltzmann equation for a two dimensional rare gas in vacuum
    • Illner R., and Pulvirenti M. Global validity of the Boltzmann equation for a two dimensional rare gas in vacuum. Comm. Math. Phys. 105 2 (1986) 189-203
    • (1986) Comm. Math. Phys. , vol.105 , Issue.2 , pp. 189-203
    • Illner, R.1    Pulvirenti, M.2
  • 98
    • 0000210546 scopus 로고
    • Global validity of the Boltzmann equation for a two-and three-dimensional rare gas in vacuum
    • Erratum and improved result
    • Erratum and improved result. Global validity of the Boltzmann equation for a two-and three-dimensional rare gas in vacuum. Comm. Math. Phys. 121 1 (1989) 143-146
    • (1989) Comm. Math. Phys. , vol.121 , Issue.1 , pp. 143-146
  • 101
    • 67649402982 scopus 로고
    • Upper bounds on the number of determining modes, nodes and volume element for the Navier-Stokes equation
    • Jones D.A., and Titi E.S. Upper bounds on the number of determining modes, nodes and volume element for the Navier-Stokes equation. Indiana Univ. Math. J. 94 (1989) 61-66
    • (1989) Indiana Univ. Math. J. , vol.94 , pp. 61-66
    • Jones, D.A.1    Titi, E.S.2
  • 102
    • 84971922576 scopus 로고
    • Negative temperature states for the two dimensional guiding-centre plasma
    • Joyce G., and Montgomery D. Negative temperature states for the two dimensional guiding-centre plasma. J. Plasma Phys. 10 (1973) 107-121
    • (1973) J. Plasma Phys. , vol.10 , pp. 107-121
    • Joyce, G.1    Montgomery, D.2
  • 103
    • 0013262044 scopus 로고
    • Smoothness of weak solutions of the Navier-Stokes equations
    • Kaniel S., and Shinbrot M. Smoothness of weak solutions of the Navier-Stokes equations. Arch. Rat. Mech. Anal. 24 (1967) 302-324
    • (1967) Arch. Rat. Mech. Anal. , vol.24 , pp. 302-324
    • Kaniel, S.1    Shinbrot, M.2
  • 104
    • 34250136481 scopus 로고
    • Remarks on the breakdown of smooth solutions for the 3-d Euler equa-tion
    • Kato T., Beale J.T., and Majda A. Remarks on the breakdown of smooth solutions for the 3-d Euler equa-tion. Comm. Math. Phys. 94 (1989) 61-66
    • (1989) Comm. Math. Phys. , vol.94 , pp. 61-66
    • Kato, T.1    Beale, J.T.2    Majda, A.3
  • 105
    • 0031224859 scopus 로고    scopus 로고
    • Vorticity filaments in two-dimensional turbulence: creation, stability and effect
    • Kevlahan N.K.-R., and Farge M. Vorticity filaments in two-dimensional turbulence: creation, stability and effect. J. Fluid Mech. 346 (1997) 49
    • (1997) J. Fluid Mech. , vol.346 , pp. 49
    • Kevlahan, N.K.-R.1    Farge, M.2
  • 107
    • 84990617895 scopus 로고
    • Commutator estimates and the Euler and Navier-Stokes equations
    • Kato T., and Ponce G. Commutator estimates and the Euler and Navier-Stokes equations. Comm. Pure Appl. Math. 41 (1988) 891-907
    • (1988) Comm. Pure Appl. Math. , vol.41 , pp. 891-907
    • Kato, T.1    Ponce, G.2
  • 108
    • 84990587445 scopus 로고
    • Statistical mechanics of classical particles with logarithmic interaction
    • Kiessling M.K.H. Statistical mechanics of classical particles with logarithmic interaction. Comm. Pure Appl. Math. 46 (1993) 27-56
    • (1993) Comm. Pure Appl. Math. , vol.46 , pp. 27-56
    • Kiessling, M.K.H.1
  • 109
    • 84980156074 scopus 로고
    • Singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids
    • Klainerman S., and Majda A. Singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids. Comm. Pure Appl. Math. 34 4 (1981) 481-524
    • (1981) Comm. Pure Appl. Math. , vol.34 , Issue.4 , pp. 481-524
    • Klainerman, S.1    Majda, A.2
  • 110
    • 84990557419 scopus 로고
    • Compressible and incompressible fluids
    • Compressible and incompressible fluids. Comm. Pure Appl. Math. 35 5 (1982) 629-651
    • (1982) Comm. Pure Appl. Math. , vol.35 , Issue.5 , pp. 629-651
  • 111
    • 0001277608 scopus 로고
    • The local structure of turbulence in incompressible viscous fluid for very large Reynolds
    • Kolmogorov A.N. The local structure of turbulence in incompressible viscous fluid for very large Reynolds. C. R. Acad. Sci. URSS 30 (1941) 301
    • (1941) C. R. Acad. Sci. URSS , vol.30 , pp. 301
    • Kolmogorov, A.N.1
  • 112
    • 67649387849 scopus 로고    scopus 로고
    • On the rate of attraction to global attractors of partial differential equations, Preprint, Univ
    • I. Kostin, On the rate of attraction to global attractors of partial differential equations, Preprint, Univ. Saint-Petersburg.
    • Saint-Petersburg
    • Kostin, I.1
  • 113
    • 36849114603 scopus 로고
    • Inertial ranges in two-dimensional turbulence
    • Kraichnan R.H. Inertial ranges in two-dimensional turbulence. Phys. Fluids 10 (1967) 1417-1423
    • (1967) Phys. Fluids , vol.10 , pp. 1417-1423
    • Kraichnan, R.H.1
  • 114
    • 0008476720 scopus 로고
    • Some modern developments in the statistical theory of turbulence
    • Rice S.A., Freed K.F., and Light J.C. (Eds)
    • Kraichnan R.H. Some modern developments in the statistical theory of turbulence. In: Rice S.A., Freed K.F., and Light J.C. (Eds). Statistical Mechanics: New Concepts, New Problems, New Applications (1972) 201-227
    • (1972) Statistical Mechanics: New Concepts, New Problems, New Applications , pp. 201-227
    • Kraichnan, R.H.1
  • 115
    • 0002859777 scopus 로고
    • Sur de nouvelles équations dans la dynamique des fluides visqueux et leu résolution globale
    • Ladyzhenskaya O.A. Sur de nouvelles équations dans la dynamique des fluides visqueux et leu résolution globale. Troudi Mat. Inst. Stekloff CII (1967) 85-104
    • (1967) Troudi Mat. Inst. Stekloff , vol.CII , pp. 85-104
    • Ladyzhenskaya, O.A.1
  • 117
    • 0000375959 scopus 로고
    • J. Soviet Math. 28 5 (1985) 714-725
    • (1985) J. Soviet Math. , vol.28 , Issue.5 , pp. 714-725
  • 120
    • 0004227821 scopus 로고
    • Attractors for Semigroups and Evolution Equations
    • Cambridge Univ. Press, Cambridge
    • Ladyzhenskaya O.A. Attractors for Semigroups and Evolution Equations. Academica Nazionale dei Lincer Series (1991), Cambridge Univ. Press, Cambridge
    • (1991) Academica Nazionale dei Lincer Series
    • Ladyzhenskaya, O.A.1
  • 121
    • 67649404465 scopus 로고
    • Course of Theoretical Physics, Vol. 5: Statistical Physics
    • Sykes J.B., and Kearsley M.J. (Eds), Pergamon Press, New York
    • Landau L., and Lifshitz E. Course of Theoretical Physics, Vol. 5: Statistical Physics. In: Sykes J.B., and Kearsley M.J. (Eds). Translated from the Russian. 2nd edn. (1968), Pergamon Press, New York
    • (1968) Translated from the Russian. 2nd edn.
    • Landau, L.1    Lifshitz, E.2
  • 123
    • 0001518823 scopus 로고
    • Time evolution of large classical systems
    • Recontres, Battelle Res. Inst, Seattle, WA
    • Lanford O. Time evolution of large classical systems. Dynamical Systems, Theory Appl. (1974), Recontres, Battelle Res. Inst, Seattle, WA 1-111
    • (1974) Dynamical Systems, Theory Appl. , pp. 1-111
    • Lanford, O.1
  • 124
    • 0004281112 scopus 로고
    • Springer, Berlin
    • Lecture Notes in Phys. Vol. 38 (1975), Springer, Berlin
    • (1975) Lecture Notes in Phys. , vol.38
  • 126
    • 0000221349 scopus 로고
    • Essai sur les mouvements plans d'un liquide visqueux que limitent des parois
    • Leray J. Essai sur les mouvements plans d'un liquide visqueux que limitent des parois. J. Math. Pures Appl. 13 (1934) 331-418
    • (1934) J. Math. Pures Appl. , vol.13 , pp. 331-418
    • Leray, J.1
  • 127
    • 51249193194 scopus 로고
    • Essai sur le mouvement d'un liquide visqueux emplissant l'espace
    • Leray J. Essai sur le mouvement d'un liquide visqueux emplissant l'espace. Acta Math. 63 (1934) 193-248
    • (1934) Acta Math. , vol.63 , pp. 193-248
    • Leray, J.1
  • 128
    • 51249193194 scopus 로고
    • Sur le mouvement d'un fluide visqueux emplissant l'espace
    • Leray J. Sur le mouvement d'un fluide visqueux emplissant l'espace. Acta Math. 63 (1934) 193-248
    • (1934) Acta Math. , vol.63 , pp. 193-248
    • Leray, J.1
  • 129
    • 0009002721 scopus 로고
    • Über einige Existenzproblem der Hydrodynamik homogener unzusammendrückbarer, rei-bunglosser Flüssikeiten und die Helmholtzschen Wirbelsalitze
    • Lichtenstein L. Über einige Existenzproblem der Hydrodynamik homogener unzusammendrückbarer, rei-bunglosser Flüssikeiten und die Helmholtzschen Wirbelsalitze. Mat. Zeit. Phys. 23 (1925) 89-154
    • (1925) Mat. Zeit. Phys. , vol.23 , pp. 89-154
    • Lichtenstein, L.1
  • 130
    • 0344077472 scopus 로고
    • Über einige Existenzproblem der Hydrodynamik homogener unzusammendrückbarer, rei-bunglosser Flüssikeiten und die Helmholtzschen Wirbelsalitze
    • Lichtenstein L. Über einige Existenzproblem der Hydrodynamik homogener unzusammendrückbarer, rei-bunglosser Flüssikeiten und die Helmholtzschen Wirbelsalitze. Mat. Zeit. Phys. 26 (1927) 193-323
    • (1927) Mat. Zeit. Phys. , vol.26 , pp. 193-323
    • Lichtenstein, L.1
  • 131
    • 2442444093 scopus 로고
    • Über einige Existenzproblem der Hydrodynamik homogener unzusammendrückbarer, rei-bunglosser Flüssikeiten und die Helmholtzschen Wirbelsalitze
    • Lichtenstein L. Über einige Existenzproblem der Hydrodynamik homogener unzusammendrückbarer, rei-bunglosser Flüssikeiten und die Helmholtzschen Wirbelsalitze. Mat. Zeit. Phys. 32 (1930) 608
    • (1930) Mat. Zeit. Phys. , vol.32 , pp. 608
    • Lichtenstein, L.1
  • 132
    • 48749147673 scopus 로고
    • p bound for the Riesz and Bessel potentials of orthonormal functions
    • p bound for the Riesz and Bessel potentials of orthonormal functions. J. Funct. Anal. 51 2 (1983) 159-165
    • (1983) J. Funct. Anal. , vol.51 , Issue.2 , pp. 159-165
    • Lieb, E.1
  • 133
    • 0032344639 scopus 로고
    • A new proof of the Caffarelli-Kohn-Nirenberg theorem
    • Lin F. A new proof of the Caffarelli-Kohn-Nirenberg theorem. Comm. Pure Appl. Math. 51 (1993) 241-257
    • (1993) Comm. Pure Appl. Math. , vol.51 , pp. 241-257
    • Lin, F.1
  • 136
    • 0000241853 scopus 로고
    • Deterministic^non periodic flow
    • Lorenz E.N. Deterministic^non periodic flow. J. Atmosph. Sci. 20 2 (1963) 130-141
    • (1963) J. Atmosph. Sci. , vol.20 , Issue.2 , pp. 130-141
    • Lorenz, E.N.1
  • 137
    • 21344481767 scopus 로고
    • A sharp lower bound for the Hausdorff dimension of the global attractors of the 2D Navier-Stokes equations
    • Liu V.X. A sharp lower bound for the Hausdorff dimension of the global attractors of the 2D Navier-Stokes equations. Comm. Math. Phys. 158 (1993) 327-339
    • (1993) Comm. Math. Phys. , vol.158 , pp. 327-339
    • Liu, V.X.1
  • 138
    • 0000812712 scopus 로고
    • Statistical mechanics of violent relaxation in stellar systems
    • Lynden-Bell D. Statistical mechanics of violent relaxation in stellar systems. Mont. Not. R. Astr. Soc. 136 (1967) 101-121
    • (1967) Mont. Not. R. Astr. Soc. , vol.136 , pp. 101-121
    • Lynden-Bell, D.1
  • 139
    • 0001684396 scopus 로고
    • Invariant helical subspaces for the Navier-Stokes equations
    • Mahalov A., Leibovich S., and Titi E. Invariant helical subspaces for the Navier-Stokes equations. Arch. Rat. Mech. Anal. 112 3 (1990) 193-222
    • (1990) Arch. Rat. Mech. Anal. , vol.112 , Issue.3 , pp. 193-222
    • Mahalov, A.1    Leibovich, S.2    Titi, E.3
  • 140
    • 0031507314 scopus 로고
    • Dissipation topography and statistical theories for large scale coherent structure
    • Majda A., and Holen M. Dissipation topography and statistical theories for large scale coherent structure. Comm. Pure Appl. Math. 50 (1987) 1183-1234
    • (1987) Comm. Pure Appl. Math. , vol.50 , pp. 1183-1234
    • Majda, A.1    Holen, M.2
  • 142
    • 0003290175 scopus 로고
    • On the dimension of the compact invariant sets of certain nonlinear maps
    • Springer, New York
    • Mañé B. On the dimension of the compact invariant sets of certain nonlinear maps. Lecture Notes in Math. Vol. 898 (1981), Springer, New York 230-242
    • (1981) Lecture Notes in Math. , vol.898 , pp. 230-242
    • Mañé, B.1
  • 143
    • 0001459179 scopus 로고
    • The dissipation range spectrum
    • Manley O.P. The dissipation range spectrum. Phys. Fluids A 4 (1992) 1320-1321
    • (1992) Phys. Fluids A , vol.4 , pp. 1320-1321
    • Manley, O.P.1
  • 144
    • 0003269966 scopus 로고    scopus 로고
    • Mathematical Theory of Incompressible Nonviscous Fluids
    • Springer, Berlin
    • Marchioro C., and Pulvirenti M. Mathematical Theory of Incompressible Nonviscous Fluids. Appl. Math. Sci. Vol. 96 (1998), Springer, Berlin
    • (1998) Appl. Math. Sci. , vol.96
    • Marchioro, C.1    Pulvirenti, M.2
  • 146
    • 0025448240 scopus 로고
    • J. Fluid Mech. 215 (1990) 393
    • (1990) J. Fluid Mech. , vol.215 , pp. 393
  • 147
    • 35949004902 scopus 로고
    • Statistical mechanics, Euler's equation and Jupiter's Red spot
    • Miller J., Weichman P.B., and Cross C. Statistical mechanics, Euler's equation and Jupiter's Red spot. Phys. Rev. A 45 4 (1992) 2328-2358
    • (1992) Phys. Rev. A , vol.45 , Issue.4 , pp. 2328-2358
    • Miller, J.1    Weichman, P.B.2    Cross, C.3
  • 148
    • 0003663481 scopus 로고
    • Lions J.L., and Ciarlet P. (Eds), Masson-Wiley, Paris
    • Mohammadi B., and Pironneau O. In: Lions J.L., and Ciarlet P. (Eds). Analysis of the K-ε Turbulence Model. Res. Appl. Math. Vol. 31 (1994), Masson-Wiley, Paris
    • (1994) Res. Appl. Math. , vol.31
    • Mohammadi, B.1    Pironneau, O.2
  • 149
    • 0000464203 scopus 로고
    • Fluid dynamic limit of the nonlinear Boltzmann equation at the level of the compressible Euler equation
    • Nishida T. Fluid dynamic limit of the nonlinear Boltzmann equation at the level of the compressible Euler equation. Comm. Math. Phys. 61 (1978) 119-168
    • (1978) Comm. Math. Phys. , vol.61 , pp. 119-168
    • Nishida, T.1
  • 150
    • 85008112960 scopus 로고
    • Global solutions to the initial value problem for the nonlinear Boltzmann equation
    • Nishida T., and Imai K. Global solutions to the initial value problem for the nonlinear Boltzmann equation. Publ. Res. Inst. Math. Sci. Kyoto Univ. 12 (1976) 229-238
    • (1976) Publ. Res. Inst. Math. Sci. Kyoto Univ. , vol.12 , pp. 229-238
    • Nishida, T.1    Imai, K.2
  • 151
    • 0141729849 scopus 로고
    • Log-corrected energy spectrum and dimension^of attractor in two-dimensional turbulence
    • Ohkitani K. Log-corrected energy spectrum and dimension^of attractor in two-dimensional turbulence. Phys. Fluids A 1 (1989) 451-452
    • (1989) Phys. Fluids A , vol.1 , pp. 451-452
    • Ohkitani, K.1
  • 152
    • 51249192666 scopus 로고
    • Statistical hydrodynamics
    • Onsager L. Statistical hydrodynamics. Suppl. Nuovo Cimento 6 (1949) 279-287
    • (1949) Suppl. Nuovo Cimento , vol.6 , pp. 279-287
    • Onsager, L.1
  • 153
    • 0001917856 scopus 로고
    • Renormalization group analysis of turbulence
    • Orszag S., and Yakhot V. Renormalization group analysis of turbulence. J. Sci. Comput. 1 (1986)
    • (1986) J. Sci. Comput. , vol.1
    • Orszag, S.1    Yakhot, V.2
  • 154
    • 0037642097 scopus 로고
    • BV estimates fail for most quasilinear hyperbolic systems in dimension greater than one
    • Rauch J. BV estimates fail for most quasilinear hyperbolic systems in dimension greater than one. Comm. Math. Phys. 106 (1986) 481-484
    • (1986) Comm. Math. Phys. , vol.106 , pp. 481-484
    • Rauch, J.1
  • 155
    • 84968467415 scopus 로고
    • Navier-Stokes equations on thin 3D domains. I: Global attractors and global regularity of solutions
    • Raugel G., and Sell G. Navier-Stokes equations on thin 3D domains. I: Global attractors and global regularity of solutions. J. Amer. Math. Soc. 6 (1993) 503-568
    • (1993) J. Amer. Math. Soc. , vol.6 , pp. 503-568
    • Raugel, G.1    Sell, G.2
  • 156
    • 33645540554 scopus 로고
    • A maximum entropy principle for two-dimensional perfect fluid dynamics
    • Robert R. A maximum entropy principle for two-dimensional perfect fluid dynamics. J. Statist. Phys. 65 (1991) 531-553
    • (1991) J. Statist. Phys. , vol.65 , pp. 531-553
    • Robert, R.1
  • 157
    • 0026202960 scopus 로고
    • Statistical equilibrium states for two dimensional flows
    • Robert R., and Sommeria J. Statistical equilibrium states for two dimensional flows. J. Fluid Mech. 229 (1991) 291-310
    • (1991) J. Fluid Mech. , vol.229 , pp. 291-310
    • Robert, R.1    Sommeria, J.2
  • 158
    • 0001768220 scopus 로고
    • An inviscidflow with compact support in space-time
    • Scheffer V. An inviscidflow with compact support in space-time. J. Geom. Anal. 3 4 (1993) 343-401
    • (1993) J. Geom. Anal. , vol.3 , Issue.4 , pp. 343-401
    • Scheffer, V.1
  • 159
    • 0000169262 scopus 로고
    • On the interior regularity of weak solutions of the Navier-Stokes equations
    • Serrin J. On the interior regularity of weak solutions of the Navier-Stokes equations. Arch. Rat. Mech. Anal. 9 (1962) 187-195
    • (1962) Arch. Rat. Mech. Anal. , vol.9 , pp. 187-195
    • Serrin, J.1
  • 160
    • 0031491102 scopus 로고    scopus 로고
    • On the nonuniqueness of weak solution of the Euler equation
    • Shnirelman A. On the nonuniqueness of weak solution of the Euler equation. Comm. Pure Appl. Math. 50 (1997) 1261-1286
    • (1997) Comm. Pure Appl. Math. , vol.50 , pp. 1261-1286
    • Shnirelman, A.1
  • 161
    • 0001628249 scopus 로고
    • Formation of singularities in compressible fluids
    • Sideris T. Formation of singularities in compressible fluids. Comm. Math. Phys. 101 (1985) 475-485
    • (1985) Comm. Math. Phys. , vol.101 , pp. 475-485
    • Sideris, T.1
  • 162
    • 0001957739 scopus 로고
    • General circulation model of the atmosphere
    • Smagorinsky J.S. General circulation model of the atmosphere. Mon. Weather Rev. 91 (1963) 99-164
    • (1963) Mon. Weather Rev. , vol.91 , pp. 99-164
    • Smagorinsky, J.S.1
  • 163
    • 0000325376 scopus 로고
    • The dissipation range spectrum and the velocity-derivative skewness in turbulent flows
    • Smith L.M., and Reynolds W.C. The dissipation range spectrum and the velocity-derivative skewness in turbulent flows. Phys. Fluids A 3 (1991) 992
    • (1991) Phys. Fluids A , vol.3 , pp. 992
    • Smith, L.M.1    Reynolds, W.C.2
  • 164
  • 166
    • 0039017057 scopus 로고
    • On the motion of a symmetric top with a cavity filled by a fluid
    • On the motion of a symmetric top with a cavity filled by a fluid. Appl. Mech. Tech. Phys. 3 (1960) 20-55
    • (1960) Appl. Mech. Tech. Phys. , vol.3 , pp. 20-55
  • 167
    • 0011968533 scopus 로고
    • On the regularity of the pressure of weak solutions of Navier-Stokes equations
    • Sohr H., and Wahl W.v. On the regularity of the pressure of weak solutions of Navier-Stokes equations. Arch. Math. (Basel) 46 (1986) 428-439
    • (1986) Arch. Math. (Basel) , vol.46 , pp. 428-439
    • Sohr, H.1    Wahl, W.v.2
  • 168
    • 0003201639 scopus 로고
    • Singular Integrals and Differentiability Properties of Functions
    • Princeton Univ. Press, Princeton, NJ
    • Stein E.M. Singular Integrals and Differentiability Properties of Functions. Princeton Math. Ser. Vol. 30 (1970), Princeton Univ. Press, Princeton, NJ
    • (1970) Princeton Math. Ser. , vol.30
    • Stein, E.M.1
  • 169
    • 0000779360 scopus 로고    scopus 로고
    • Detecting strange attractors in turbulence
    • D.A Raud and L.S. Young, eds, Springer, Berlin
    • F. Takens, Detecting strange attractors in turbulence, D.A Raud and L.S. Young, eds, Lecture Notes in Math., Vol. 898, Springer, Berlin.
    • Lecture Notes in Math , vol.898
    • Takens, F.1
  • 170
    • 84974050752 scopus 로고
    • H-measures a new approach for studying homogeneization, oscillations and concentration^ef-fects in partial differential equations
    • Tartar L. H-measures a new approach for studying homogeneization, oscillations and concentration^ef-fects in partial differential equations. Proc. Roy. Soc. Edinburgh Sect. A 115 (1990) 193-230
    • (1990) Proc. Roy. Soc. Edinburgh Sect. A , vol.115 , pp. 193-230
    • Tartar, L.1
  • 172
    • 0003278399 scopus 로고
    • Infinite-Dimensional Dynamical Systems in Mechanics and Physics
    • Springer, New York
    • Temam R. Infinite-Dimensional Dynamical Systems in Mechanics and Physics. Appl. Math. Sci. Vol. 68 (1988), Springer, New York
    • (1988) Appl. Math. Sci. , vol.68
    • Temam, R.1
  • 173
    • 0009328610 scopus 로고
    • Les solutions globales de l'équation de Boltzmann dans l'espace tout entier et dans le demi espace
    • Ukai S. Les solutions globales de l'équation de Boltzmann dans l'espace tout entier et dans le demi espace. C. R. Acad. Sci. Paris A 282 (1976) 317-320
    • (1976) C. R. Acad. Sci. Paris A , vol.282 , pp. 317-320
    • Ukai, S.1
  • 174
    • 0012074805 scopus 로고    scopus 로고
    • L'équation de Hopf, les solutions statistiques les moments correspondants aux systèmes des équations paraboliques quasilinéaires
    • Vishik M.I., and Fursikov A.V. L'équation de Hopf, les solutions statistiques les moments correspondants aux systèmes des équations paraboliques quasilinéaires. J. Math. Pures Appl. 9-56 1 (1997) 85-122
    • (1997) J. Math. Pures Appl. , vol.9-56 , Issue.1 , pp. 85-122
    • Vishik, M.I.1    Fursikov, A.V.2
  • 175
    • 0343545071 scopus 로고    scopus 로고
    • Solutions statistiques homogènes des systèmes différentiels paraboliques et du système de Navier-Stokes
    • Vishik M.I., and Fursikov A.V. Solutions statistiques homogènes des systèmes différentiels paraboliques et du système de Navier-Stokes. Ann. Scuola. Norm. Sup. Pisa Cl. Sci. 3-4 (1997) 531-576
    • (1997) Ann. Scuola. Norm. Sup. Pisa Cl. Sci. , vol.3-4 , pp. 531-576
    • Vishik, M.I.1    Fursikov, A.V.2
  • 176
    • 0042096887 scopus 로고    scopus 로고
    • Translationally homogeneous statistical solutions and individual solutions with infinite energy of a system of Navier-Stokes equations
    • Vishik M.I., and Fursikov A.V. Translationally homogeneous statistical solutions and individual solutions with infinite energy of a system of Navier-Stokes equations. Sibirsk. Math. J. 5-19 1 (1998) 1005-1031
    • (1998) Sibirsk. Math. J. , vol.5-19 , Issue.1 , pp. 1005-1031
    • Vishik, M.I.1    Fursikov, A.V.2
  • 179
    • 34250940791 scopus 로고
    • Un théorème sur l'existence du mouvement plan d'un fluide parfait, homogène^et incom-pressible, pendant^un temps infiniment long
    • Wolibner W. Un théorème sur l'existence du mouvement plan d'un fluide parfait, homogène^et incom-pressible, pendant^un temps infiniment long. Mat. Z. 37 (1933) 698-726
    • (1933) Mat. Z. , vol.37 , pp. 698-726
    • Wolibner, W.1
  • 180
    • 0001751564 scopus 로고
    • Non stationary flow of an ideal incompressible liquid
    • Yudovich V.I. Non stationary flow of an ideal incompressible liquid. Zh. Vych. Mat. 3 (1963) 1032-1066
    • (1963) Zh. Vych. Mat. , vol.3 , pp. 1032-1066
    • Yudovich, V.I.1


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