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Volumn 66, Issue 11, 2007, Pages 2427-2458

Viscosity versus vorticity stretching: Global well-posedness for a family of Navier-Stokes-alpha-like models

Author keywords

Existence; Fluid mechanics; Regularity theory; Turbulence; Uniqueness

Indexed keywords

FLUID MECHANICS; LAPLACE TRANSFORMS; MATHEMATICAL MODELS; TURBULENCE; VISCOSITY; VORTEX FLOW;

EID: 33847363573     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2006.03.030     Document Type: Article
Times cited : (77)

References (57)
  • 2
    • 0003924563 scopus 로고
    • Van Nostrand, Princeton, NJ Prepared for publication by B. Frank Jones Jr., with the assistance of George W. Batten Jr
    • Agmon S. Lectures on Elliptic Boundary Value Problems (1965), Van Nostrand, Princeton, NJ Prepared for publication by B. Frank Jones Jr., with the assistance of George W. Batten Jr
    • (1965) Lectures on Elliptic Boundary Value Problems
    • Agmon, S.1
  • 5
    • 0026791799 scopus 로고
    • Phenomenological behavior of multipolar viscous fluids
    • Bellout H., Bloom F., and Nečas J. Phenomenological behavior of multipolar viscous fluids. Quart. Appl. Math. 1 3 (1992) 559-583
    • (1992) Quart. Appl. Math. , vol.1 , Issue.3 , pp. 559-583
    • Bellout, H.1    Bloom, F.2    Nečas, J.3
  • 7
    • 49149142420 scopus 로고
    • Nonlinear Schrödinger evolution equations
    • Brézis H., and Gallouet T. Nonlinear Schrödinger evolution equations. Nonlinear Anal. 4 (1980) 677-681
    • (1980) Nonlinear Anal. , vol.4 , pp. 677-681
    • Brézis, H.1    Gallouet, T.2
  • 8
    • 28644438663 scopus 로고    scopus 로고
    • On the Clark-α model of turbulence: Global regularity and long-time dynamics
    • Cao C., Holm D.D., and Titi E.S. On the Clark-α model of turbulence: Global regularity and long-time dynamics. J. Turbul. 6 20 (2005) 1-11
    • (2005) J. Turbul. , vol.6 , Issue.20 , pp. 1-11
    • Cao, C.1    Holm, D.D.2    Titi, E.S.3
  • 9
    • 0001262719 scopus 로고    scopus 로고
    • Camassa-Holm equations as a closure model for turbulent channel and pipe flow
    • Chen S., Foias C., Holm D.D., Olson E., Titi E.S., and Wynne S. Camassa-Holm equations as a closure model for turbulent channel and pipe flow. Phys. Rev. Lett. 81 (1998) 5338-5341
    • (1998) Phys. Rev. Lett. , vol.81 , pp. 5338-5341
    • Chen, S.1    Foias, C.2    Holm, D.D.3    Olson, E.4    Titi, E.S.5    Wynne, S.6
  • 10
    • 0032614269 scopus 로고    scopus 로고
    • A connection between the Camassa-Holm equations and turbulent flows in channels and pipes
    • The International Conference on Turbulence (Los Alamos, NM, 1998)
    • Chen S., Foias C., Holm D.D., Olson E., Titi E.S., and Wynne S. A connection between the Camassa-Holm equations and turbulent flows in channels and pipes. The International Conference on Turbulence (Los Alamos, NM, 1998). Phys. Fluids 11 (1999) 2343-2353
    • (1999) Phys. Fluids , vol.11 , pp. 2343-2353
    • Chen, S.1    Foias, C.2    Holm, D.D.3    Olson, E.4    Titi, E.S.5    Wynne, S.6
  • 11
    • 0039964945 scopus 로고    scopus 로고
    • The Camassa-Holm equations and turbulence
    • Predictability: Quantifying uncertainty in models of complex phenomena (Los Alamos, NM, 1998)
    • Chen S., Foias C., Holm D.D., Olson E., Titi E.S., and Wynne S. The Camassa-Holm equations and turbulence. Predictability: Quantifying uncertainty in models of complex phenomena (Los Alamos, NM, 1998). Physica D 133 (1999) 49-65
    • (1999) Physica D , vol.133 , pp. 49-65
    • Chen, S.1    Foias, C.2    Holm, D.D.3    Olson, E.4    Titi, E.S.5    Wynne, S.6
  • 12
    • 0041152039 scopus 로고    scopus 로고
    • Direct numerical simulations of the Navier-Stokes alpha model
    • Chen S., Holm D.D., Margolin L.G., and Zhang R. Direct numerical simulations of the Navier-Stokes alpha model. Physica D 133 1-4 (1999) 66-83
    • (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
  • 13
    • 0038053956 scopus 로고    scopus 로고
    • Turbulent boundary layer equations
    • Cheskidov A. Turbulent boundary layer equations. C. R. Math. Acad. Sci. Paris 334 (2002) 423-427
    • (2002) C. R. Math. Acad. Sci. Paris , vol.334 , pp. 423-427
    • Cheskidov, A.1
  • 15
    • 33847389498 scopus 로고    scopus 로고
    • A. Cheskidov, E. Olson, E.S. Titi, The Brandina model and other α turbulence closures: A comparison study, private communication
  • 19
    • 0028976767 scopus 로고
    • Exponential decay rate of the power spectrum for solutions of the Navier-Stokes equations
    • Doering C.R., and Titi E.S. Exponential decay rate of the power spectrum for solutions of the Navier-Stokes equations. Phys. Fluids 7 6 (1995) 1384-1390
    • (1995) Phys. Fluids , vol.7 , Issue.6 , pp. 1384-1390
    • Doering, C.R.1    Titi, E.S.2
  • 21
    • 0029289811 scopus 로고
    • Fluids of differential type, critical review and thermodynamic analysis
    • Dunn J.E., and Rajagopal K.R. Fluids of differential type, critical review and thermodynamic analysis. Int. J. Eng. Sci. 33 5 (1995) 689-729
    • (1995) Int. J. Eng. Sci. , vol.33 , Issue.5 , pp. 689-729
    • Dunn, J.E.1    Rajagopal, K.R.2
  • 22
    • 0002062139 scopus 로고    scopus 로고
    • Gevrey regularity for nonlinear analytic parabolic equations
    • Ferrari A.B., and Titi E.S. Gevrey regularity for nonlinear analytic parabolic equations. Comm. Partial Differential Equations 23 1-2 (1998) 1-16
    • (1998) Comm. Partial Differential Equations , vol.23 , Issue.1-2 , pp. 1-16
    • Ferrari, A.B.1    Titi, E.S.2
  • 23
    • 0035873331 scopus 로고    scopus 로고
    • The Navier-Stokes-alpha model of fluid turbulence
    • Foias C., Holm D.D., and Titi E.S. The Navier-Stokes-alpha model of fluid turbulence. Physica D 152-153 (2001) 505-519
    • (2001) Physica D , vol.152-153 , pp. 505-519
    • Foias, C.1    Holm, D.D.2    Titi, E.S.3
  • 24
    • 36749037534 scopus 로고    scopus 로고
    • The three dimensional viscous Camassa-Holm equations, and their relation to the Navier-Stokes equations and turbulence theory
    • Foias C., Holm D.D., and Titi E.S. The three dimensional viscous Camassa-Holm equations, and their relation to the Navier-Stokes equations and turbulence theory. J. Dynam. Differential Equations 14 (2002) 1-35
    • (2002) J. Dynam. Differential Equations , vol.14 , pp. 1-35
    • Foias, C.1    Holm, D.D.2    Titi, E.S.3
  • 25
    • 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. (9) 58 3 (1979) 339-368
    • (1979) J. Math. Pures Appl. (9) , vol.58 , Issue.3 , pp. 339-368
    • Foias, C.1    Temam, R.2
  • 26
    • 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 2 (1989) 359-369
    • (1989) J. Funct. Anal. , vol.87 , Issue.2 , pp. 359-369
    • Foias, C.1    Temam, R.2
  • 27
    • 33847356199 scopus 로고    scopus 로고
    • B.J. Guerts, D.D. Holm, Leray simulation of turbulent shear layers, in: Adv. in Turbulence IX: Proc. 9th European Turbulence Conf. Barcelona: CIMNE, 2002, pp. 337-340
  • 28
    • 0037279812 scopus 로고    scopus 로고
    • Regularization modeling for large-eddy simulation
    • Guerts B.J., and Holm D.D. Regularization modeling for large-eddy simulation. Phys. Fluids 15 (2003) L13-L16
    • (2003) Phys. Fluids , vol.15
    • Guerts, B.J.1    Holm, D.D.2
  • 29
    • 0040951221 scopus 로고    scopus 로고
    • Fluctuation effects on 3D Lagrangian mean and Eulerian mean fluid motion. Predictability: Quantifying uncertainty in models of complex phenomena
    • Holm D.D. Fluctuation effects on 3D Lagrangian mean and Eulerian mean fluid motion. Predictability: Quantifying uncertainty in models of complex phenomena. Physica D 133 1-4 (1999) 215-269
    • (1999) Physica D , vol.133 , Issue.1-4 , pp. 215-269
    • Holm, D.D.1
  • 30
    • 0037174480 scopus 로고    scopus 로고
    • Kármán-Howarth theorem for the Lagrangian-averaged Navier-Stokes-alpha model of turbulence
    • Holm D.D. Kármán-Howarth theorem for the Lagrangian-averaged Navier-Stokes-alpha model of turbulence. J. Fluid Mech. 467 (2002) 205-214
    • (2002) J. Fluid Mech. , vol.467 , pp. 205-214
    • Holm, D.D.1
  • 32
    • 11744318899 scopus 로고    scopus 로고
    • Euler-Poincaré models of ideal fluids with nonlinear dispersion
    • Holm D.D., Marsden J.E., and Ratiu T.S. Euler-Poincaré models of ideal fluids with nonlinear dispersion. Phys. Rev. Lett. 80 (1998) 4173-4177
    • (1998) Phys. Rev. Lett. , vol.80 , pp. 4173-4177
    • Holm, D.D.1    Marsden, J.E.2    Ratiu, T.S.3
  • 33
    • 0001971504 scopus 로고    scopus 로고
    • The Euler-Poincaré equations and semidirect products with applications to continuum theories
    • Holm D.D., Marsden J.E., and Ratiu T.S. The Euler-Poincaré equations and semidirect products with applications to continuum theories. Adv. Math. 137 1 (1998) 1-81
    • (1998) Adv. Math. , vol.137 , Issue.1 , pp. 1-81
    • Holm, D.D.1    Marsden, J.E.2    Ratiu, T.S.3
  • 34
    • 3042653856 scopus 로고    scopus 로고
    • Boundary effects on exact solutions of the Lagrangian-averaged Navier-Stokes-α equations
    • Holm D.D., Putkaradze V., Weidman P.D., and Wingate B.A. Boundary effects on exact solutions of the Lagrangian-averaged Navier-Stokes-α equations. J. Stat. Phys. 113 5-6 (2003) 841-854
    • (2003) J. Stat. Phys. , vol.113 , Issue.5-6 , pp. 841-854
    • Holm, D.D.1    Putkaradze, V.2    Weidman, P.D.3    Wingate, B.A.4
  • 35
    • 33847349931 scopus 로고    scopus 로고
    • A.A. Ilyin, E.M. Lunasin, E.S. Titi, A modified Leray-α subgrid scale model of turbulence, preprint
  • 37
    • 0035402775 scopus 로고    scopus 로고
    • Existence of global attractor for the three-dimensional modified Navier-Stokes equations
    • Ju N. Existence of global attractor for the three-dimensional modified Navier-Stokes equations. Nonlinearity 14 (2002) 777-786
    • (2002) Nonlinearity , vol.14 , pp. 777-786
    • Ju, N.1
  • 38
    • 0007173972 scopus 로고    scopus 로고
    • Some results on modifications of three-dimensional Navier-Stokes equations
    • Springer, New York
    • Ladyzhenskaya O. Some results on modifications of three-dimensional Navier-Stokes equations. Nonlinear Analysis and Continuum Mechanics (1998), Springer, New York 73-84
    • (1998) Nonlinear Analysis and Continuum Mechanics , pp. 73-84
    • Ladyzhenskaya, O.1
  • 39
    • 0002859777 scopus 로고
    • New equations for the description of the motions of viscous incompressible fluids and global solvability for their boundary value problems
    • Ladyzhenskaya O. New equations for the description of the motions of viscous incompressible fluids and global solvability for their boundary value problems. Trudy Mat. Inst. Steklov. 102 (1967) 85-104
    • (1967) Trudy Mat. Inst. Steklov. , vol.102 , pp. 85-104
    • Ladyzhenskaya, O.1
  • 41
    • 0039272584 scopus 로고
    • Quelques résultats d'existence dans des équations aux dérivées partielles non linéaires
    • Lions J.L. Quelques résultats d'existence dans des équations aux dérivées partielles non linéaires. Bull. Soc. Math. France 87 (1959) 245-273
    • (1959) Bull. Soc. Math. France , vol.87 , pp. 245-273
    • Lions, J.L.1
  • 44
    • 0030594509 scopus 로고    scopus 로고
    • A finite-dimensional attractor for three-dimensional flow of incompressible fluids
    • Málek J., and Nečas J. A finite-dimensional attractor for three-dimensional flow of incompressible fluids. J. Differential Equations 127 (1996) 498-518
    • (1996) J. Differential Equations , vol.127 , pp. 498-518
    • Málek, J.1    Nečas, J.2
  • 45
    • 0038111248 scopus 로고    scopus 로고
    • Global well-posedness for the Lagrangian averaged Navier-Stokes (LANS-α) equations on bounded domains
    • Marsden J.E., and Shkoller S. Global well-posedness for the Lagrangian averaged Navier-Stokes (LANS-α) equations on bounded domains. R. Soc. Lond. Philos. Trans. Ser. A Math. Phys. Eng. Sci. 359 (2001) 1449-1468
    • (2001) R. Soc. Lond. Philos. Trans. Ser. A Math. Phys. Eng. Sci. , vol.359 , pp. 1449-1468
    • Marsden, J.E.1    Shkoller, S.2
  • 46
    • 0001505107 scopus 로고    scopus 로고
    • Multidimensional advection and fractional dispersion
    • Meerschaert M.M., Benson D.A., and Baeumer B. Multidimensional advection and fractional dispersion. Phys. Rev. E 59 (1999) 5026-5028
    • (1999) Phys. Rev. E , vol.59 , pp. 5026-5028
    • Meerschaert, M.M.1    Benson, D.A.2    Baeumer, B.3
  • 47
    • 18344370872 scopus 로고    scopus 로고
    • Operator Lévy motion and multiscaling anomalous diffusion
    • Meerschaert M.M., Benson D.A., and Baeumer B. Operator Lévy motion and multiscaling anomalous diffusion. Phys. Rev. E 63 (2001) 021112
    • (2001) Phys. Rev. E , vol.63 , pp. 021112
    • Meerschaert, M.M.1    Benson, D.A.2    Baeumer, B.3
  • 49
    • 0003987999 scopus 로고    scopus 로고
    • Cambridge University Press
    • Pope S.B. Turbulent Flows (2003), Cambridge University Press
    • (2003) Turbulent Flows
    • Pope, S.B.1
  • 50
    • 33847361167 scopus 로고    scopus 로고
    • J. Robinson, Infinite-Dimensional Dynamical Systems: An Introduction to Dissipative Parabolic PDEs and the Theory of Global Attractors, in: Cambridge Texts in Applied Mathematics, 2001
  • 52
    • 0001957739 scopus 로고
    • General circulation experiments with the primitive equations
    • Smagorinsky J. General circulation experiments with the primitive equations. Mon. Weather Rev. 93 (1963) 99-164
    • (1963) Mon. Weather Rev. , vol.93 , pp. 99-164
    • Smagorinsky, J.1
  • 53
    • 0042355118 scopus 로고
    • Existence of solutions of a mathematical model of a nonlinear viscous liquid
    • Sobolevskii P.E. Existence of solutions of a mathematical model of a nonlinear viscous liquid. Dokl. Acad. Nauk SSSR 285 (1985) 44-48
    • (1985) Dokl. Acad. Nauk SSSR , vol.285 , pp. 44-48
    • Sobolevskii, P.E.1
  • 55
    • 0037210213 scopus 로고    scopus 로고
    • On some modifications of Navier-Stokes equations
    • Soltanov K.N. On some modifications of Navier-Stokes equations. Nonlinear Anal. 52 (2003) 769-793
    • (2003) Nonlinear Anal. , vol.52 , pp. 769-793
    • Soltanov, K.N.1
  • 57
    • 17444393974 scopus 로고    scopus 로고
    • Trajectory attractor approximations of the 3D Navier-Stokes system by a Leray-α model
    • (Translated from Russian)
    • Vishik M.I., Titi E.S., and Chepyzhov V.V. Trajectory attractor approximations of the 3D Navier-Stokes system by a Leray-α model. Russian Math. Dokl. 71 (2005) 92-95 (Translated from Russian)
    • (2005) Russian Math. Dokl. , vol.71 , pp. 92-95
    • Vishik, M.I.1    Titi, E.S.2    Chepyzhov, V.V.3


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