A remark on smooth solutions of the weakly compressible periodic Navier-Stokes equations

Kyoto Journal of Mathematics

Volumn 40, Issue 3, 2000, Pages 525-540

  Gallagher, Isabelle ^a  

^a UNIVERSITÉ PARIS SACLAY   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034558779     PISSN: 0023608X     EISSN: None     Source Type: Journal    
DOI: 10.1215/kjm/1250517679     Document Type: Article

References (18)

1. J.-Y. Chemin, About the Navier-Stokes System, preprint of the Laboratoire d'Analyse Numérique, Paris 6, 1996.
2. R. Danchin, Global Existence in Critical Spaces for Compressible Navier-Stokes Equations, preprint of the Laboratoire d'Analyse Numérique, Paris 6, 1999, to appear in Inventiones Mathematicae.
3. B. Desjardins and E. Grenier, Low Mach Number Limit of Viscous Compressible Flows in the Whole Space, Proceedings of the Royal Society of London A, 455 (1999), 2271-2279.
4. B. Desjardins, E. Grenier, P.-L. Lions and N. Masmoudi, Incompressible Limit for Solutions of the Isentropic Navier-Stokes Equations with Dirichlet Boundary Conditions, Journal de Mathématiques Pures et Appliquées, 78 (1999), 461-471.
5. I. Gallagher, Asymptotics of the Solutions of Hyperbolic Equations With a Skew-Symmetric Perturbation, Journal of Differential Equations, 150 (1998), 363-384.
6. I. Gallagher, Applications of Schochet's Methods to Parabolic Equations, Journal de Mathématiques Pures et Appliquées, 77 (1998), 989-1054.
7. E. Grenier, Oscillatory Perturbations of the Navier-Stokes Equations, Journal de Mathématiques Pures et Appliquées, 76 (1997), 477-498.
8. T. Hagstrom and J. Lorenz, All-Time Existence of Classical Solutions for Slightly Compressible Flows, SIAM Journal of Mathematical Analysis, 28 (1998), 652-672.
9. J.-L. JoIy, G. Métivier and J. Rauch, Generic Rigorous Asymptotic Expansions for Weakly Nonlinear Multidimensional Oscillatory Waves, Duke Mathematical Journal, 70 (1993), 373-404.
10. S. Klainerman and A. Majda, Compressible and Incompressible Fluids, Communications on Pure and Applied Mathematics 35 (1982), 629-651.
11. H.-O. Kreiss and J. Lorenz, Initial-Boundary Value Problems and the Navier-Stokes Equations, Academic Press, New York, 1989.
12. H.-O. Kreiss, J. Lorenz and M.J. Naughton, Convergence of the Solutions of the Compressible to the Solutions of the Incompressible Navier-Stokes Equations, Advances in Pure and Applied Mathematics, 12 (1991), 187-214.
13. P.-L. Lions, Mathematical Topics in Fluid Mechanics, Vol. I,Incompressible Models, and Vol. II, Compressible Models, Oxford University Press, 1998.
14. P.-L. Lions and N. Masmoudi, Incompressible Limit for a Viscous Compressible Fluid, Journal de Mathématiques Pures et Appliquées, 77 (1998), 585-627.
15. A. Majda, Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables, Applied Mathematical Sciences, 53, Springer Verlag, New York, 1984.
16. C. Marchioro and M. Pulvirenti, Mathematical Theory of Incompressible Nonviscous Fluids, Applied Mathematical Sciences, 96, Springer Verlag, New York, 1994.
17. S. Schochet, Fast Singular Limits of Hyperbolic PDEs, Journal of Differential Equations, 114 (1994), 476-512.
18. S. Ukai, The Incompressible Limit and the Initial Layer of the Compressible Euler Equation, J. Math. Kyoto Univ., 26 (1986), 323-331.