메뉴 건너뛰기




Volumn 212, Issue 3, 2014, Pages 875-903

Absence of Anomalous Dissipation of Energy in Forced Two Dimensional Fluid Equations

Author keywords

[No Author keywords available]

Indexed keywords


EID: 84897940249     PISSN: 00039527     EISSN: 14320673     Source Type: Journal    
DOI: 10.1007/s00205-013-0708-7     Document Type: Article
Times cited : (34)

References (80)
  • 1
    • 61849151015 scopus 로고    scopus 로고
    • On the global well-posedness of the critical quasi-geostrophic equation
    • Abidi H., Hmidi T.: On the global well-posedness of the critical quasi-geostrophic equation. SIAM J. Math. Anal., 40(1), 167-185 (2008).
    • (2008) SIAM J. Math. Anal. , vol.40 , Issue.1 , pp. 167-185
    • Abidi, H.1    Hmidi, T.2
  • 2
    • 34250136481 scopus 로고
    • Remarks on the breakdown of smooth solutions for the 3-D Euler equations
    • Beale J. T., Kato T., Majda A.: Remarks on the breakdown of smooth solutions for the 3-D Euler equations. Comm. Math. Phys., 94(1), 61-66 (1984).
    • (1984) Comm. Math. Phys. , vol.94 , Issue.1 , pp. 61-66
    • Beale, J.T.1    Kato, T.2    Majda, A.3
  • 3
    • 4544330532 scopus 로고    scopus 로고
    • Vanishing viscosity limit and long-time behavior for 2D quasi-geostrophic equations
    • Berselli L. C.: Vanishing viscosity limit and long-time behavior for 2D quasi-geostrophic equations. Indiana Univ. Math. J., 51(4), 905-930 (2002).
    • (2002) Indiana Univ. Math. J. , vol.51 , Issue.4 , pp. 905-930
    • Berselli, L.C.1
  • 4
    • 77950869887 scopus 로고    scopus 로고
    • Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation
    • Caffarelli, L. A., Vasseur, A.: Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation. Ann. Math. (2), 171(3), 1903-1930 (2010).
    • (2010) Ann. Math. (2) , vol.171 , Issue.3 , pp. 1903-1930
    • Caffarelli, L.A.1    Vasseur, A.2
  • 5
    • 79953027828 scopus 로고    scopus 로고
    • The De Giorgi method for regularity of solutions of elliptic equations and its applications to fluid dynamics
    • Caffarelli L. A., Vasseur A. F.: The De Giorgi method for regularity of solutions of elliptic equations and its applications to fluid dynamics. Discrete Contin. Dyn. Syst. Ser. S, 3(3), 409-427 (2010).
    • (2010) Discrete Contin. Dyn. Syst. Ser. S , vol.3 , Issue.3 , pp. 409-427
    • Caffarelli, L.A.1    Vasseur, A.F.2
  • 6
    • 54749092935 scopus 로고    scopus 로고
    • The geometric approaches to the possible singularities in the inviscid fluid flows
    • 11
    • Chae, D.: The geometric approaches to the possible singularities in the inviscid fluid flows. J. Phys. A, 41(36), 365501, 11 (2008).
    • (2008) J. Phys. A , vol.41 , Issue.36 , pp. 365501
    • Chae, D.1
  • 7
    • 0037330176 scopus 로고    scopus 로고
    • Global well-posedness in the super-critical dissipative quasi-geostrophic equations
    • Chae D., Lee J.: Global well-posedness in the super-critical dissipative quasi-geostrophic equations. Commun. Math. Phys., 233(2), 297-311 (2003).
    • (2003) Commun. Math. Phys. , vol.233 , Issue.2 , pp. 297-311
    • Chae, D.1    Lee, J.2
  • 8
    • 33947403194 scopus 로고    scopus 로고
    • A new Bernstein's inequality and the 2D dissipative quasi-geostrophic equation. Commun
    • Chen Q., Miao C., Zhang Z.: A new Bernstein's inequality and the 2D dissipative quasi-geostrophic equation. Commun. Math. Phys., 271(3), 821-838 (2007).
    • (2007) Math. Phys. , vol.271 , Issue.3 , pp. 821-838
    • Chen, Q.1    Miao, C.2    Zhang, Z.3
  • 9
    • 45149096278 scopus 로고    scopus 로고
    • Energy conservation and Onsager's conjecture for the Euler equations
    • Cheskidov A., Constantin P., Friedlander S., Shvydkoy R.: Energy conservation and Onsager's conjecture for the Euler equations. Nonlinearity, 21(6), 1233-1252 (2008).
    • (2008) Nonlinearity , vol.21 , Issue.6 , pp. 1233-1252
    • Cheskidov, A.1    Constantin, P.2    Friedlander, S.3    Shvydkoy, R.4
  • 10
    • 0001212876 scopus 로고
    • Note on loss of regularity for solutions of the 3-D incompressible Euler and related equations
    • Constantin P.: Note on loss of regularity for solutions of the 3-D incompressible Euler and related equations. Commun. Math. Phys., 104(2), 311-326 (1986).
    • (1986) Commun. Math. Phys. , vol.104 , Issue.2 , pp. 311-326
    • Constantin, P.1
  • 11
    • 0037191442 scopus 로고    scopus 로고
    • Energy spectrum of quasigeostrophic turbulence
    • Constantin P.: Energy spectrum of quasigeostrophic turbulence. Phys. Rev. Lett., 89(18), 184501 (2002).
    • (2002) Phys. Rev. Lett. , vol.89 , Issue.18 , pp. 184501
    • Constantin, P.1
  • 13
    • 0002223508 scopus 로고    scopus 로고
    • On the critical dissipative quasi-geostrophic equation
    • Dedicated to Professors Ciprian Foias and Roger Temam (Bloomington, IN, 2000)
    • Constantin, P., Cordoba, D., Wu, J.: On the critical dissipative quasi-geostrophic equation. Indiana Univ. Math. J., 50(Special Issue), 97-107 (2001). Dedicated to Professors Ciprian Foias and Roger Temam (Bloomington, IN, 2000).
    • (2001) Indiana Univ. Math. J. , vol.50 , Issue.SPEC. ISSUE , pp. 97-107
    • Constantin, P.1    Cordoba, D.2    Wu, J.3
  • 14
    • 21844522201 scopus 로고
    • Onsager's conjecture on the energy conservation for solutions of Euler's equation
    • Constantin P., Weinan E., Titi E. S.: Onsager's conjecture on the energy conservation for solutions of Euler's equation. Comm. Math. Phys., 165(1), 207-209 (1994).
    • (1994) Comm. Math. Phys. , vol.165 , Issue.1 , pp. 207-209
    • Constantin, P.1    Weinan, E.2    Titi, E.S.3
  • 15
    • 0003241585 scopus 로고
    • Navier-Stokes equations
    • University of Chicago Press, Chicago, IL
    • Constantin, P., Foias, C.: Navier-Stokes equations. In: Chicago Lectures in Mathematics. University of Chicago Press, Chicago, IL, (1988).
    • (1988) Chicago Lectures in Mathematics
    • Constantin, P.1    Foias, C.2
  • 16
    • 84855663746 scopus 로고    scopus 로고
    • New numerical results for the surface quasi-geostrophic equation
    • Constantin P., Lai M.-C., Sharma R., Tseng Y.-H., Wu J.: New numerical results for the surface quasi-geostrophic equation. J. Sci. Comput., 50(1), 1-28 (2012).
    • (2012) J. Sci. Comput. , vol.50 , Issue.1 , pp. 1-28
    • Constantin, P.1    Lai, M.-C.2    Sharma, R.3    Tseng, Y.-H.4    Wu, J.5
  • 17
    • 0043172071 scopus 로고
    • Formation of strong fronts in the 2-D quasigeostrophic thermal active scalar
    • Constantin P., Majda A. J., Tabak E.: Formation of strong fronts in the 2-D quasigeostrophic thermal active scalar. Nonlinearity, 7(6), 1495-1533 (1994).
    • (1994) Nonlinearity , vol.7 , Issue.6 , pp. 1495-1533
    • Constantin, P.1    Majda, A.J.2    Tabak, E.3
  • 18
    • 0000579087 scopus 로고    scopus 로고
    • Nonsingular surface quasi-geostrophic flow
    • Constantin P., Nie Q., Schörghofer N.: Nonsingular surface quasi-geostrophic flow. Phys. Lett. A, 241(3), 168-172 (1998).
    • (1998) Phys. Lett. A , vol.241 , Issue.3 , pp. 168-172
    • Constantin, P.1    Nie, Q.2    Schörghofer, N.3
  • 21
    • 84868156364 scopus 로고    scopus 로고
    • Nonlinear maximum principles for dissipative linear nonlocal operators and applications
    • Constantin P., Vicol V.: Nonlinear maximum principles for dissipative linear nonlocal operators and applications. Geom. Funct. Anal., 22(5), 1289-1321 (2012).
    • (2012) Geom. Funct. Anal. , vol.22 , Issue.5 , pp. 1289-1321
    • Constantin, P.1    Vicol, V.2
  • 22
    • 0033419179 scopus 로고    scopus 로고
    • Behavior of solutions of 2D quasi-geostrophic equations
    • Constantin P., Wu J.: Behavior of solutions of 2D quasi-geostrophic equations. SIAM J. Math. Anal., 30(5), 937-948 (1999).
    • (1999) SIAM J. Math. Anal. , vol.30 , Issue.5 , pp. 937-948
    • Constantin, P.1    Wu, J.2
  • 23
    • 54549116855 scopus 로고    scopus 로고
    • Regularity of Hölder continuous solutions of the supercritical quasi-geostrophic equation
    • Constantin P., Wu J.: Regularity of Hölder continuous solutions of the supercritical quasi-geostrophic equation. Ann. Inst. H. Poincaré Anal. Non Linéaire, 25(6), 1103-1110 (2008).
    • (2008) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.25 , Issue.6 , pp. 1103-1110
    • Constantin, P.1    Wu, J.2
  • 24
    • 58249085827 scopus 로고    scopus 로고
    • Hölder continuity of solutions of supercritical dissipative hydrodynamic transport equations
    • Constantin P., Wu J.: Hölder continuity of solutions of supercritical dissipative hydrodynamic transport equations. Ann. Inst. H. Poincaré Anal. Non Linéaire, 26(1), 159-180 (2009).
    • (2009) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.26 , Issue.1 , pp. 159-180
    • Constantin, P.1    Wu, J.2
  • 25
    • 4544377751 scopus 로고    scopus 로고
    • A maximum principle applied to quasi-geostrophic equations
    • Córdoba A., Córdoba D.: A maximum principle applied to quasi-geostrophic equations. Commun. Math. Phys., 249(3), 511-528 (2004).
    • (2004) Commun. Math. Phys. , vol.249 , Issue.3 , pp. 511-528
    • Córdoba, A.1    Córdoba, D.2
  • 26
    • 0032264533 scopus 로고    scopus 로고
    • Nonexistence of simple hyperbolic blow-up for the quasi-geostrophic equation
    • Córdoba, D.: Nonexistence of simple hyperbolic blow-up for the quasi-geostrophic equation. Ann. Math. (2), 148(3), 1135-1152 (1998).
    • (1998) Ann. Math. (2) , vol.148 , Issue.3 , pp. 1135-1152
    • Córdoba, D.1
  • 27
    • 0035836678 scopus 로고    scopus 로고
    • Behavior of several two-dimensional fluid equations in singular scenarios
    • Córdoba D., Fefferman C.: Behavior of several two-dimensional fluid equations in singular scenarios. Proc. Natl. Acad. Sci. USA, 98(8), 4311-4312 (2001).
    • (2001) Proc. Natl. Acad. Sci. USA , vol.98 , Issue.8 , pp. 4311-4312
    • Córdoba, D.1    Fefferman, C.2
  • 28
    • 0036016138 scopus 로고    scopus 로고
    • Growth of solutions for QG and 2D Euler equations
    • Córdoba, D., Fefferman, C.: Growth of solutions for QG and 2D Euler equations. J. Am. Math. Soc., 15(3), 665-670 (2002).
    • (2002) J. Am. Math. Soc. , vol.15 , Issue.3 , pp. 665-670
    • Córdoba, D.1    Fefferman, C.2
  • 29
    • 17844380780 scopus 로고    scopus 로고
    • Evidence of singularities for a family of contour dynamics equations
    • Córdoba, D., Fontelos, M. A., Mancho, A. M., Rodrigo, J. L.: Evidence of singularities for a family of contour dynamics equations. Proc. Natl. Acad. Sci. USA, 102(17), 5949-5952 (2005).
    • (2005) Proc. Natl. Acad. Sci. USA , vol.102 , Issue.17 , pp. 5949-5952
    • Córdoba, D.1    Fontelos, M.A.2    Mancho, A.M.3    Rodrigo, J.L.4
  • 30
    • 79751532095 scopus 로고    scopus 로고
    • Eventual regularity of the solutions to the supercritical dissipative quasi-geostrophic equation
    • Dabkowski M.: Eventual regularity of the solutions to the supercritical dissipative quasi-geostrophic equation. Geom. Funct. Anal., 21(1), 1-13 (2011).
    • (2011) Geom. Funct. Anal. , vol.21 , Issue.1 , pp. 1-13
    • Dabkowski, M.1
  • 32
    • 84862095067 scopus 로고    scopus 로고
    • Global well-posedness for a slightly supercritical surface quasi-geostrophic equation
    • Dabkowski M., Kiselev A., Vicol V.: Global well-posedness for a slightly supercritical surface quasi-geostrophic equation. Nonlinearity, 25(5), 1525-1535 (2012).
    • (2012) Nonlinearity , vol.25 , Issue.5 , pp. 1525-1535
    • Dabkowski, M.1    Kiselev, A.2    Vicol, V.3
  • 33
    • 61749096010 scopus 로고    scopus 로고
    • On the asymptotic behavior of average energy and enstrophy in 3D turbulent flows
    • Dascaliuc R., Foias C., Jolly M. S.: On the asymptotic behavior of average energy and enstrophy in 3D turbulent flows. Phys. D, 238(7), 725-736 (2009).
    • (2009) Phys. D , vol.238 , Issue.7 , pp. 725-736
    • Dascaliuc, R.1    Foias, C.2    Jolly, M.S.3
  • 34
    • 73549114234 scopus 로고    scopus 로고
    • Estimates on enstrophy, palinstrophy, and invariant measures for 2-D turbulence
    • Dascaliuc R., Foias C., Jolly M. S.: Estimates on enstrophy, palinstrophy, and invariant measures for 2-D turbulence. J. Differ. Equ., 248(4), 792-819 (2010).
    • (2010) J. Differ. Equ. , vol.248 , Issue.4 , pp. 792-819
    • Dascaliuc, R.1    Foias, C.2    Jolly, M.S.3
  • 36
    • 71749114913 scopus 로고    scopus 로고
    • The Euler equations as a differential inclusion
    • De Lellis, C., Székelyhidi, Jr. L.: The Euler equations as a differential inclusion. Ann. Math. (2), 170(3), 1417-1436 (2009).
    • (2009) Ann. Math. (2) , vol.170 , Issue.3 , pp. 1417-1436
    • De Lellis, C.1    Székelyhidi Jr., L.2
  • 37
    • 70350655922 scopus 로고    scopus 로고
    • On admissibility criteria for weak solutions of the Euler equations
    • De Lellis, C., Székelyhidi, Jr. L.: On admissibility criteria for weak solutions of the Euler equations. Arch. Ration. Mech. Anal., 195(1), 225-260 (2010).
    • (2010) Arch. Ration. Mech. Anal. , vol.195 , Issue.1 , pp. 225-260
    • De Lellis, C.1    Székelyhidi Jr., L.2
  • 38
    • 84863104319 scopus 로고    scopus 로고
    • The h-principle and the equations of fluid dynamics
    • De Lellis, C., Székelyhidi, Jr. L.: The h-principle and the equations of fluid dynamics. Bull. Am. Math. Soc. (N. S.), 49(3), 347-375 (2012).
    • (2012) Bull. Am. Math. Soc. (N. S.) , vol.49 , Issue.3 , pp. 347-375
    • De Lellis, C.1    Székelyhidi Jr., L.2
  • 40
    • 70350569716 scopus 로고    scopus 로고
    • Level set dynamics and the non-blowup of the 2D quasi-geostrophic equation
    • Deng J., Hou T. Y., Li R., Yu X.: Level set dynamics and the non-blowup of the 2D quasi-geostrophic equation. Methods Appl. Anal., 13(2), 157-180 (2006).
    • (2006) Methods Appl. Anal. , vol.13 , Issue.2 , pp. 157-180
    • Deng, J.1    Hou, T.Y.2    Li, R.3    Yu, X.4
  • 41
    • 0037174473 scopus 로고    scopus 로고
    • Energy dissipation in body-forced turbulence
    • Doering C. R., Foias C.: Energy dissipation in body-forced turbulence. J. Fluid Mech., 467, 289-306 (2002).
    • (2002) J. Fluid Mech. , vol.467 , pp. 289-306
    • Doering, C.R.1    Foias, C.2
  • 42
    • 77950223071 scopus 로고    scopus 로고
    • Dissipative quasi-geostrophic equations in critical Sobolev spaces: smoothing effect and global well-posedness. Discrete Contin
    • Dong H.: Dissipative quasi-geostrophic equations in critical Sobolev spaces: smoothing effect and global well-posedness. Discrete Contin. Dyn. Syst., 26(4), 1197-1211 (2010).
    • (2010) Dyn. Syst. , vol.26 , Issue.4 , pp. 1197-1211
    • Dong, H.1
  • 43
    • 50249090960 scopus 로고    scopus 로고
    • Global well-posedness and a decay estimate for the critical dissipative quasi-geostrophic equation in the whole space
    • Dong H., Du D.: Global well-posedness and a decay estimate for the critical dissipative quasi-geostrophic equation in the whole space. Discrete Contin. Dyn. Syst., 21(4), 1095-1101 (2008).
    • (2008) Discrete Contin. Dyn. Syst. , vol.21 , Issue.4 , pp. 1095-1101
    • Dong, H.1    Du, D.2
  • 44
    • 43749097438 scopus 로고    scopus 로고
    • Spatial analyticity of the solutions to the subcritical dissipative quasi-geostrophic equations
    • Dong H., Li D.: Spatial analyticity of the solutions to the subcritical dissipative quasi-geostrophic equations. Arch. Ration. Mech. Anal., 189(1), 131-158 (2008).
    • (2008) Arch. Ration. Mech. Anal. , vol.189 , Issue.1 , pp. 131-158
    • Dong, H.1    Li, D.2
  • 45
    • 70349918312 scopus 로고    scopus 로고
    • Regularity criteria for the dissipative quasi-geostrophic equations in Hölder spaces. Commun
    • Dong H., Pavlović N.: Regularity criteria for the dissipative quasi-geostrophic equations in Hölder spaces. Commun. Math. Phys., 290(3), 801-812 (2009).
    • (2009) Math. Phys. , vol.290 , Issue.3 , pp. 801-812
    • Dong, H.1    Pavlović, N.2
  • 46
    • 69749083481 scopus 로고    scopus 로고
    • A regularity criterion for the dissipative quasi-geostrophic equations
    • Dong H., Pavlović N.: A regularity criterion for the dissipative quasi-geostrophic equations. Ann. Inst. H. Poincaré Anal. Non Linéaire, 26(5), 1607-1619 (2009).
    • (2009) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.26 , Issue.5 , pp. 1607-1619
    • Dong, H.1    Pavlović, N.2
  • 47
    • 0002205604 scopus 로고
    • Energy dissipation without viscosity in ideal hydrodynamics i. fourier analysis and local energy transfer
    • Eyink G. L.: Energy dissipation without viscosity in ideal hydrodynamics i. fourier analysis and local energy transfer. Physica D Nonlinear Phenomena, 78(3), 222-240 (1994).
    • (1994) Physica D Nonlinear Phenomena , vol.78 , Issue.3 , pp. 222-240
    • Eyink, G.L.1
  • 48
    • 20844435594 scopus 로고    scopus 로고
    • Locality of turbulent cascades
    • Eyink G. L.: Locality of turbulent cascades. Phys. D, 207(1-2), 91-116 (2005).
    • (2005) Phys. D , vol.207 , Issue.1-2 , pp. 91-116
    • Eyink, G.L.1
  • 49
    • 33244455644 scopus 로고    scopus 로고
    • Onsager and the theory of hydrodynamic turbulence
    • Eyink G. L., Sreenivasan K. R.: Onsager and the theory of hydrodynamic turbulence. Rev. Modern Phys., 78(1), 87-135 (2006).
    • (2006) Rev. Modern Phys. , vol.78 , Issue.1 , pp. 87-135
    • Eyink, G.L.1    Sreenivasan, K.R.2
  • 50
    • 79952484503 scopus 로고    scopus 로고
    • Analytic sharp fronts for the surface quasi-geostrophic equation
    • Fefferman C., Rodrigo J. L.: Analytic sharp fronts for the surface quasi-geostrophic equation. Commun. Math. Phys., 303(1), 261-288 (2011).
    • (2011) Commun. Math. Phys. , vol.303 , Issue.1 , pp. 261-288
    • Fefferman, C.1    Rodrigo, J.L.2
  • 51
    • 84862205918 scopus 로고    scopus 로고
    • Almost sharp fronts for SQG: the limit equations
    • Fefferman C., Rodrigo J. L.: Almost sharp fronts for SQG: the limit equations. Commun. Math. Phys., 313(1), 131-153 (2012).
    • (2012) Commun. Math. Phys. , vol.313 , Issue.1 , pp. 131-153
    • Fefferman, C.1    Rodrigo, J.L.2
  • 52
    • 0000358588 scopus 로고
    • Statistical study of Navier-Stokes equations. I
    • Foiaş C.: Statistical study of Navier-Stokes equations. I. Rend. Sem. Mat. Univ. Padova, 48, 219-348 (1972).
    • (1972) Rend. Sem. Mat. Univ. Padova , vol.48 , pp. 219-348
    • Foiaş, C.1
  • 53
    • 0002187572 scopus 로고
    • Statistical study of Navier-Stokes equations. II
    • Foiaş C.: Statistical study of Navier-Stokes equations. II. Rend. Sem. Mat. Univ. Padova, 49, 9-123 (1973).
    • (1973) Rend. Sem. Mat. Univ. Padova , vol.49 , pp. 9-123
    • Foiaş, C.1
  • 54
    • 70350580506 scopus 로고    scopus 로고
    • Nonlinear instability for the critically dissipative quasi-geostrophic equation
    • Friedlander S., Pavlović N., Vicol V.: Nonlinear instability for the critically dissipative quasi-geostrophic equation. Commun. Math. Phys., 292(3), 797-810 (2009).
    • (2009) Commun. Math. Phys. , vol.292 , Issue.3 , pp. 797-810
    • Friedlander, S.1    Pavlović, N.2    Vicol, V.3
  • 55
    • 0004185784 scopus 로고
    • Cambridge University Press, Cambridge. The legacy of A. N. Kolmogorov
    • Frisch, U.: Turbulence. Cambridge University Press, Cambridge, 1995. The legacy of A. N. Kolmogorov.
    • (1995) Turbulence
    • Frisch, U.1
  • 56
    • 84872183605 scopus 로고    scopus 로고
    • A two-dimensional vortex condensate at high Reynolds number
    • Gallet B., Young W. R.: A two-dimensional vortex condensate at high Reynolds number. J. Fluid Mech., 715, 359-388 (2013).
    • (2013) J. Fluid Mech. , vol.715 , pp. 359-388
    • Gallet, B.1    Young, W.R.2
  • 58
    • 34447123394 scopus 로고    scopus 로고
    • Global solutions of the super-critical 2D quasi-geostrophic equation in Besov spaces
    • Hmidi T., Keraani S.: Global solutions of the super-critical 2D quasi-geostrophic equation in Besov spaces. Adv. Math., 214(2), 618-638 (2007).
    • (2007) Adv. Math. , vol.214 , Issue.2 , pp. 618-638
    • Hmidi, T.1    Keraani, S.2
  • 60
    • 11144329539 scopus 로고    scopus 로고
    • Existence and uniqueness of the solution to the dissipative 2D quasi-geostrophic equations in the Sobolev space
    • Ju N.: Existence and uniqueness of the solution to the dissipative 2D quasi-geostrophic equations in the Sobolev space. Commun. Math. Phys., 251(2), 365-376 (2004).
    • (2004) Commun. Math. Phys. , vol.251 , Issue.2 , pp. 365-376
    • Ju, N.1
  • 61
    • 21244497902 scopus 로고    scopus 로고
    • The maximum principle and the global attractor for the dissipative 2D quasi-geostrophic equations
    • Ju N.: The maximum principle and the global attractor for the dissipative 2D quasi-geostrophic equations. Commun. Math. Phys., 255(1), 161-181 (2005).
    • (2005) Commun. Math. Phys. , vol.255 , Issue.1 , pp. 161-181
    • Ju, N.1
  • 62
    • 34247536873 scopus 로고    scopus 로고
    • Dissipative 2D quasi-geostrophic equation: local well-posedness, global regularity and similarity solutions
    • Ju N.: Dissipative 2D quasi-geostrophic equation: local well-posedness, global regularity and similarity solutions. Indiana Univ. Math. J., 56(1), 187-206 (2007).
    • (2007) Indiana Univ. Math. J. , vol.56 , Issue.1 , pp. 187-206
    • Ju, N.1
  • 63
    • 79956367250 scopus 로고    scopus 로고
    • Nonlocal maximum principles for active scalars
    • Kiselev A.: Nonlocal maximum principles for active scalars. Adv. Math., 227(5), 1806-1826 (2011).
    • (2011) Adv. Math. , vol.227 , Issue.5 , pp. 1806-1826
    • Kiselev, A.1
  • 65
    • 75149114116 scopus 로고    scopus 로고
    • Global regularity for the critical dispersive dissipative surface quasi-geostrophic equation
    • Kiselev A., Nazarov F.: Global regularity for the critical dispersive dissipative surface quasi-geostrophic equation. Nonlinearity, 23(3), 549-554 (2010).
    • (2010) Nonlinearity , vol.23 , Issue.3 , pp. 549-554
    • Kiselev, A.1    Nazarov, F.2
  • 66
    • 33846785446 scopus 로고    scopus 로고
    • Global well-posedness for the critical 2D dissipative quasi-geostrophic equation
    • Kiselev A., Nazarov F., Volberg A.: Global well-posedness for the critical 2D dissipative quasi-geostrophic equation. Invent. Math., 167(3), 445-453 (2007).
    • (2007) Invent. Math. , vol.167 , Issue.3 , pp. 445-453
    • Kiselev, A.1    Nazarov, F.2    Volberg, A.3
  • 68
    • 33846833851 scopus 로고    scopus 로고
    • Remarks about the inviscid limit of the Navier-Stokes system
    • Masmoudi N.: Remarks about the inviscid limit of the Navier-Stokes system. Commun. Math. Phys., 270(3), 777-788 (2007).
    • (2007) Commun. Math. Phys. , vol.270 , Issue.3 , pp. 777-788
    • Masmoudi, N.1
  • 69
    • 33747198457 scopus 로고    scopus 로고
    • Dissipative quasi-geostrophic equation for large initial data in the critical Sobolev space
    • Miura H.: Dissipative quasi-geostrophic equation for large initial data in the critical Sobolev space. Commun. Math. Phys., 267(1), 141-157 (2006).
    • (2006) Commun. Math. Phys. , vol.267 , Issue.1 , pp. 141-157
    • Miura, H.1
  • 70
    • 78650136818 scopus 로고    scopus 로고
    • Oscillatory damping in long-time evolution of the surface quasi-geostrophic equations with generalized viscosity: a numerical study
    • Ohkitani K., Sakajo T.: Oscillatory damping in long-time evolution of the surface quasi-geostrophic equations with generalized viscosity: a numerical study. Nonlinearity, 23(12), 3029-3051 (2010).
    • (2010) Nonlinearity , vol.23 , Issue.12 , pp. 3029-3051
    • Ohkitani, K.1    Sakajo, T.2
  • 71
    • 0030876020 scopus 로고    scopus 로고
    • Inviscid and inviscid-limit behavior of a surface quasigeostrophic flow
    • Ohkitani K., Yamada M.: Inviscid and inviscid-limit behavior of a surface quasigeostrophic flow. Phys. Fluids, 9(4), 876-882 (1997).
    • (1997) Phys. Fluids , vol.9 , Issue.4 , pp. 876-882
    • Ohkitani, K.1    Yamada, M.2
  • 73
    • 1642618627 scopus 로고    scopus 로고
    • Asymptotic behavior to dissipative quasi-geostrophic flows
    • Schonbek M. E., Schonbek T. P.: Asymptotic behavior to dissipative quasi-geostrophic flows. SIAM J. Math. Anal., 35(2), 357-375 (2003).
    • (2003) SIAM J. Math. Anal. , vol.35 , Issue.2 , pp. 357-375
    • Schonbek, M.E.1    Schonbek, T.P.2
  • 74
    • 76849110369 scopus 로고    scopus 로고
    • Eventual regularization for the slightly supercritical quasi-geostrophic equation
    • Silvestre L.: Eventual regularization for the slightly supercritical quasi-geostrophic equation. Ann. Inst. H. Poincaré Anal. Non Linéaire, 27(2), 693-704 (2010).
    • (2010) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.27 , Issue.2 , pp. 693-704
    • Silvestre, L.1
  • 75
    • 0000569640 scopus 로고    scopus 로고
    • The phenomenology of small-scale turbulence
    • Annu. Rev. Fluid Mech., vol. 29. Annual Reviews, Palo Alto, CA
    • Sreenivasan, K. R., Antonia, R. A.: The phenomenology of small-scale turbulence. In: Annual review of fluid mechanics, Vol. 29. Annu. Rev. Fluid Mech., vol. 29. Annual Reviews, Palo Alto, CA, 435-472, (1997).
    • (1997) Annual review of fluid mechanics , vol.29 , pp. 435-472
    • Sreenivasan, K.R.1    Antonia, R.A.2
  • 78
    • 18744399570 scopus 로고    scopus 로고
    • Global solutions of the 2D dissipative quasi-geostrophic equation in Besov spaces
    • (2004/05, electronic)
    • Wu, J.: Global solutions of the 2D dissipative quasi-geostrophic equation in Besov spaces. SIAM J. Math. Anal., 36(3), 1014-1030 (2004/05, electronic).
    • SIAM J. Math. Anal. , vol.36 , Issue.3 , pp. 1014-1030
    • Wu, J.1
  • 79
    • 84860610382 scopus 로고    scopus 로고
    • Note on the well-posedness of a slightly supercritical surface quasi-geostrophic equation
    • Xue L., Zheng X.: Note on the well-posedness of a slightly supercritical surface quasi-geostrophic equation. J. Differ. Equ., 253(2), 795-813 (2012).
    • (2012) J. Differ. Equ. , vol.253 , Issue.2 , pp. 795-813
    • Xue, L.1    Zheng, X.2
  • 80
    • 35248823548 scopus 로고    scopus 로고
    • Remarks on the global regularity for the super-critical 2D dissipative quasi-geostrophic equation
    • Yu X.: Remarks on the global regularity for the super-critical 2D dissipative quasi-geostrophic equation. J. Math. Anal. Appl., 339(1), 359-371 (2008).
    • (2008) J. Math. Anal. Appl. , vol.339 , Issue.1 , pp. 359-371
    • Yu, X.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.