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Volumn 4, Issue 4, 2006, Pages 823-848

GLOBAL WELL-POSEDNESS OF THE THREE-DIMENSIONAL VISCOUS AND INVISCID SIMPLIFIED BARDINA TURBULENCE MODELS

Author keywords

Global attractors; Inviscid regularization of euler equations; Large eddy simulations; Sub grid scale models; Turbulence models

Indexed keywords


EID: 40749110015     PISSN: 15396746     EISSN: 19450796     Source Type: Journal    
DOI: 10.4310/CMS.2006.v4.n4.a8     Document Type: Article
Times cited : (205)

References (46)
  • 1
    • 0003796630 scopus 로고
    • [1] Academic Press, New York
    • [1] R. A. Adams, Sobolev Spaces, Academic Press, New York, 1975.
    • (1975) Sobolev Spaces
    • Adams, R. A.1
  • 5
    • 2142717291 scopus 로고    scopus 로고
    • On the fractal dimension of invariant set; applications to Navier-Stokes equations
    • [5]
    • [5] V. V. Chepyzhov and A. A. Ilyin, On the fractal dimension of invariant set; applications to Navier-Stokes equations, Discrete Continuous Dynamical Systems, 10, 117-135, 2004.
    • (2004) Discrete Continuous Dynamical Systems , vol.10 , pp. 117-135
    • Chepyzhov, V. V.1    Ilyin, A. A.2
  • 7
    • 0032614269 scopus 로고    scopus 로고
    • A connection between the Camassa-Holm equations and turbulent flows in channels and pipes
    • [7]
    • [7] S. Chen, C. Foias, D. D. Holm, E. Olson, E. S. Titi and S. Wynne, A connection between the Camassa-Holm equations and turbulent flows in channels and pipes, Phys. Fluids, 11(8), 2343-2353, 1999.
    • (1999) Phys. Fluids , vol.11 , Issue.8 , pp. 2343-2353
    • Chen, S.1    Foias, C.2    Holm, D. D.3    Olson, E.4    Titi, E. S.5    Wynne, S.6
  • 8
    • 0001262719 scopus 로고    scopus 로고
    • Camassa-Holm equations as a closure model for turbulent channel and pipe flow
    • [8]
    • [8] S. Chen, C. Foias, D. D. Holm, E. Olson, E. S. Titi and S. Wynne, Camassa-Holm equations as a closure model for turbulent channel and pipe flow, Phys. Rev. Lett., 81(24), 5338-5341, 1998.
    • (1998) Phys. Rev. Lett , vol.81 , Issue.24 , pp. 5338-5341
    • Chen, S.1    Foias, C.2    Holm, D. D.3    Olson, E.4    Titi, E. S.5    Wynne, S.6
  • 9
    • 0041152039 scopus 로고    scopus 로고
    • Direct numerical simulations of the Navier-Stokes alpha model
    • [9]
    • [9] S. Chen, D. D. Holm, L. G. Margolin and R. Zhang, Direct numerical simulations of the Navier-Stokes alpha model, Physica D, 133(1-4), 66-83, 1999.
    • (1999) Physica D , vol.133 , Issue.1-4 , pp. 66-83
    • Chen, S.1    Holm, D. D.2    Margolin, L. G.3    Zhang, R.4
  • 11
    • 28644438663 scopus 로고    scopus 로고
    • On the Clark-® model of turbulence: global regularity and long-time dynamics
    • [11]
    • [11] C. Cao, D. Holm and E. S. Titi, On the Clark-® model of turbulence: global regularity and long-time dynamics, Journal of Turbulence, 6(20), 1-11, 2005.
    • (2005) Journal of Turbulence , vol.6 , Issue.20 , pp. 1-11
    • Cao, C.1    Holm, D.2    Titi, E. S.3
  • 12
    • 84990581938 scopus 로고
    • Global Lyapunov exponents, Kaplan-Yorke formulas and the di-mension of the attractors for 2D Navier-Stokes equations
    • [12]
    • [12] P. Constantin and C. Foias, Global Lyapunov exponents, Kaplan-Yorke formulas and the di-mension of the attractors for 2D Navier-Stokes equations, Comm. Pure Apl. Math., 38(1), 1-27, 1985.
    • (1985) Comm. Pure Apl. Math , vol.38 , Issue.1 , pp. 1-27
    • Constantin, P.1    Foias, C.2
  • 15
    • 0001300072 scopus 로고    scopus 로고
    • What do the Navier-Stokes equations tell us about turbulence? Harmonic Analysis and Nonlinear Differential Equations Riverside, CA, 151-180, 1995
    • [15] Contemp. Math., Amer. Math. Soc., Providence, RI, 1997
    • [15] C. Foias, What do the Navier-Stokes equations tell us about turbulence? Harmonic Analysis and Nonlinear Differential Equations Riverside, CA, 151-180, 1995, Contemp. Math., Amer. Math. Soc., Providence, RI, 208, 1997.
    • , vol.208
    • Foias, C.1
  • 16
    • 36749037534 scopus 로고    scopus 로고
    • The three dimensional viscous Camassa-Holm equa-tions, and their relation to the Navier-Stokes equations and turbulence theory
    • [16]
    • [16] C. Foias, D. D. Holm and E. S. Titi, The three dimensional viscous Camassa-Holm equa-tions, and their relation to the Navier-Stokes equations and turbulence theory, J. Dynam. Differential Equations, 14, 1-35, 2002.
    • (2002) J. Dynam. Differential Equations , vol.14 , pp. 1-35
    • Foias, C.1    Holm, D. D.2    Titi, E. S.3
  • 17
    • 0035873331 scopus 로고    scopus 로고
    • The Navier-Stokes-alpha model of fluid turbulence.Advances in nonlinear mathematics and science
    • [17]
    • [17] C. Foias, D. D. Holm and E. S. Titi, The Navier-Stokes-alpha model of fluid turbulence.Advances in nonlinear mathematics and science, Physica D, 152/153, 505-519, 2001.
    • (2001) Physica D , vol.152 , Issue.153 , pp. 505-519
    • Foias, C.1    Holm, D. D.2    Titi, E. S.3
  • 19
    • 0040951221 scopus 로고    scopus 로고
    • Fluctuation effect on 3D-Lagrangian mean and Eulerian mean fluidmotion
    • [19]
    • [19] B. Geurts and D. Holm, Fluctuation effect on 3D-Lagrangian mean and Eulerian mean fluidmotion, Physica D, 133, 215-269, 1999.
    • (1999) Physica D , vol.133 , pp. 215-269
    • Geurts, B.1    Holm, D.2
  • 20
    • 0037279812 scopus 로고    scopus 로고
    • Regularization modeling for large eddy simulation
    • [20]
    • [20] B. Geurts and D. Holm, Regularization modeling for large eddy simulation, Physics of Fluids,15, L13-L16, 2003.
    • (2003) Physics of Fluids , vol.15 , pp. L13-L16
    • Geurts, B.1    Holm, D.2
  • 21
    • 33746725258 scopus 로고    scopus 로고
    • Length-scale estimates for the LANS-® equations in terms of theReynolds number
    • [21]
    • [21] J. Gibbon and D. Holm, Length-scale estimates for the LANS-® equations in terms of theReynolds number, Physica D, 220, 69-78, 2006.
    • (2006) Physica D , vol.220 , pp. 69-78
    • Gibbon, J.1    Holm, D.2
  • 23
    • 11744318899 scopus 로고    scopus 로고
    • Euler-Poincaré models of ideal fluids with nonlinear dispersion
    • [23]
    • [23] D. Holm and T. Ratiu Marsden, Euler-Poincaré models of ideal fluids with nonlinear dispersion,Phys. Rev. Lett., 80, 4173-4176, 1998.
    • (1998) Phys. Rev. Lett , vol.80 , pp. 4173-4176
    • Holm, D.1    Ratiu Marsden, T.2
  • 24
    • 0442281584 scopus 로고    scopus 로고
    • Modeling mesoscale turbulence in the barotropic double-gyre circula-tion
    • [24]
    • [24] D. Holm and B. Nadiga, Modeling mesoscale turbulence in the barotropic double-gyre circula-tion, Journal of Physical Oceanography, 33(11), 2355-2365, 2003.
    • (2003) Journal of Physical Oceanography , vol.33 , Issue.11 , pp. 2355-2365
    • Holm, D.1    Nadiga, B.2
  • 25
    • 84867933671 scopus 로고    scopus 로고
    • Dynamic depletion of vortex stretching and non-blowup of the 3-Dincompressible Euler Equations
    • [25]
    • [25] T. Y. Hou and R. Li, Dynamic depletion of vortex stretching and non-blowup of the 3-Dincompressible Euler Equations, J. Nonlinear Science, 16(6), 639-664, 2006.
    • (2006) J. Nonlinear Science , vol.16 , Issue.6 , pp. 639-664
    • Hou, T. Y.1    Li, R.2
  • 26
    • 33645065343 scopus 로고    scopus 로고
    • A modified-Leray-a subgrid scale model of turbulence
    • [26]
    • [26] A. Ilyin, E. Lunasin and E. S. Titi, A modified-Leray-a subgrid scale model of turbulence,Nonlinearity, 19, 879-897, 2006.
    • (2006) Nonlinearity , vol.19 , pp. 879-897
    • Ilyin, A.1    Lunasin, E.2    Titi, E. S.3
  • 27
    • 0009183050 scopus 로고
    • Attractors for some nonlinear problems of mathematical physics
    • [27] Kraev. Zadachi Mat. Fiz. i Smezhnye Vopr. Teor. Funktsii18, 182, 50-54; translation in J. Soviet Math., 40(5), 619-622, 1988
    • [27] V. K. Kalantarov, Attractors for some nonlinear problems of mathematical physics, Russian,Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov (LOMI), 152, 1986, Kraev. Zadachi Mat. Fiz. i Smezhnye Vopr. Teor. Funktsii18, 182, 50-54; translation in J. Soviet Math., 40(5), 619-622, 1988.
    • (1986) Russian,Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov (LOMI) , vol.152
    • Kalantarov, V. K.1
  • 29
    • 0002859777 scopus 로고
    • New equations for the description of motion of viscous incompressible uids and solvability in the large of boundary value problems for them
    • [29]
    • [29] O. A. Ladyzhenskaya, New equations for the description of motion of viscous incompressible uids and solvability in the large of boundary value problems for them, Proc. Steklov Insts. Math., 102, 95-118, 1967.
    • (1967) Proc. Steklov Insts. Math , vol.102 , pp. 95-118
    • Ladyzhenskaya, O. A.1
  • 32
    • 0002624077 scopus 로고
    • Inequalities for the moments of the eigenvalues of the Schringer Hamiltonian and their relation to Sobolev inequalities
    • [32] Bargman eds. E. Lieb, B. Simon, and A. S. Wightman, Princeton University Press, Princeton, New Jersey
    • [32] E. Lieb and W. Thirring, Inequalities for the moments of the eigenvalues of the Schringer Hamiltonian and their relation to Sobolev inequalities, Studies in Mathematical Physics: Essays in Honor of V. Bargman eds. E. Lieb, B. Simon, and A. S. Wightman, Princeton University Press, Princeton, New Jersey, 226-303, 1976.
    • (1976) Studies in Mathematical Physics: Essays in Honor of V , pp. 226-303
    • Lieb, E.1    Thirring, W.2
  • 33
    • 0039272584 scopus 로고
    • Quelques resultats d 'existence dans des equations aux dérivées partielles non linéaires
    • [33]
    • [33] J. L. Lions, Quelques resultats d 'existence dans des equations aux dérivées partielles non linéaires, Bull. Soc. Math. France, 87, 245-273, 1959.
    • (1959) Bull. Soc. Math. France , vol.87 , pp. 245-273
    • Lions, J. L.1
  • 35
    • 0037331178 scopus 로고    scopus 로고
    • Numerical simulations of the Lagrangian averaged Navier-Stokes equations for homogeneous isotropic turbulence
    • [35]
    • [35] K. Mohseni, B. Kosovic, S. Shkoller and J. Marsden, Numerical simulations of the Lagrangian averaged Navier-Stokes equations for homogeneous isotropic turbulence, Phys. Fluids, 15(2), 524-544, 2003.
    • (2003) Phys. Fluids , vol.15 , Issue.2 , pp. 524-544
    • Mohseni, K.1    Kosovic, B.2    Shkoller, S.3    Marsden, J.4
  • 36
    • 85128803336 scopus 로고    scopus 로고
    • Viscosity versus vorticity stretching: global well-posedness for a family of Navier-Stokes-alpha-like models
    • [36] to appear
    • [36] E. Olson and E. S. Titi, Viscosity versus vorticity stretching: global well-posedness for a family of Navier-Stokes-alpha-like models, Math. Anal. Ser. A: Theory Methods, to appear.
    • Math. Anal. Ser. A: Theory Methods
    • Olson, E.1    Titi, E. S.2
  • 37
    • 52849140426 scopus 로고
    • The uniqueness and solvability in the large of boundary value problems for the equations of motion of aqueous solutions of polymers, Russian, Boundary Value Problems of Mathematical Physics and Related Questions in the Theory of Functions
    • [37] 7
    • [37] A. P. Oskolkov, The uniqueness and solvability in the large of boundary value problems for the equations of motion of aqueous solutions of polymers, Russian, Boundary Value Problems of Mathematical Physics and Related Questions in the Theory of Functions, 7 Zap. Naucn. Sem. Leninggrad. Otdel. Mat. Inst. Steklov. (LOMI), 38, 98-136, 1973.
    • (1973) Zap. Naucn. Sem. Leninggrad. Otdel. Mat. Inst. Steklov. (LOMI) , vol.38 , pp. 98-136
    • Oskolkov, A. P.1
  • 38
    • 0003987999 scopus 로고    scopus 로고
    • [38] Cambridge University Press
    • [38] S. Pope, Turbulent Flows, Cambridge University Press, 2001.
    • (2001) Turbulent Flows
    • Pope, S.1
  • 40
    • 0001766450 scopus 로고
    • Valeurs propes d'operateurs definis par la restriction de systemes variationelles a des sous-espaces
    • [40]
    • [40] G. Metivier, Valeurs propes d'operateurs definis par la restriction de systemes variationelles a des sous-espaces, J. Math. Pures Appl., 57(9), 133-156, 1978.
    • (1978) J. Math. Pures Appl , vol.57 , Issue.9 , pp. 133-156
    • Metivier, G.1
  • 43
    • 0001957739 scopus 로고
    • General circulation experiments with the primitive equations. I. The basic experiment
    • [43]
    • [43] J. Smagorinsky, General circulation experiments with the primitive equations. I. The basic experiment, Mon. Weather Rev., 91-99, 1963.
    • (1963) Mon. Weather Rev , pp. 91-99
    • Smagorinsky, J.1


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