On the Stability of Boundary Layers of Incompressible Euler Equations

Journal of Differential Equations

Volumn 164, Issue 1, 2000, Pages 180-222

  Grenier, E ^a,b  

^a CNRS   (France)

^b ECOLE NORMALE SUPÉRIEURE   (France)

Author keywords

Fluid mechanics; Euler equations; stability; boundary layers; M canique des fluides; quations d'Euler; stabilit ; couches limites

Indexed keywords

EID: 0037889795     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1006/jdeq.1999.3713     Document Type: Article

References (23)

1. V. I. Arnold, Méthodes mathématiques de la mécanique classique, Mir.
2. Arnold V. I. Sur la géométrie différentielle des groupes de Lie de dimension infinie et ses applications à l'hydrodynamique des fluides parfaits. Ann. Institut Fourier. 16:1996;319-361.
3. Y. Brenier, Reformulations of some inviscid hydrostatic models, manuscript, 1997.
4. R. E. Caflisch, and, M. Sanmartino, Zero viscosity limit for analytic solutions of the Navier-Stokes equation on a half-space. I. Existence for Euler and Prandtl equations, preprint.
5. R. E. Caflisch, and, M. Sanmartino, Zero viscosity limit for analytic solutions of the Navier-Stokes equation on a half-space. II. Construction of the Navier-Stokes solution, preprint.
6. B. Desjardins, and, E. Grenier, On the homogeneous model of wind driven ocean circulation, preprint, 1997.
7. Drazin P. G., Reid W. H. Hydrodynamic Stability. Cambridge Monographs on Mechanics and Applied Mathematics. 1981.
8. W. E. B. Engquist, Blow up of solutions to the unsteady Prandtl equations, preprint, 1996.
9. Friedlander S., Strauss W., Vishik M. Nonlinear instability in an ideal fluid. Ann. Inst. H. Poincaré Anal. Non Linéaire. 14:1997;187-209.
10. Guo Y., Strauss W. Nonlinear instability of double-humped equilibria. Ann. Inst. H. Poincaré Anal. Non Linéaire. 12:1995;339-352.
11. Greenspan H. P. The Theory of Rotating Fluids. Cambridge Monographs on Mechanics and Applied Mathematics. 1969.
12. E. Grenier, Boundary layers of characteristic nonlinear parabolic equations, J. Math. Pures Appl, to appear.
13. E. Grenier, On the instability of boundary layers of incompressible Navier Stokes equations, in preparation.
14. E. Grenier, and, O. Guès, On the inviscid limit of noncharacteristic nonlinear parabolic systems, J. Differential Equations, to appear.
15. Grenier E., Masmoudi N. Ekman layers of rotating fluids, the case of well prepared initial data. Comm. Partial Differential Equations. 22:1997;953-975.
16. Hoskins B. J. The geostrophic momentum approximation and the semi-geostrophic equations. J. Atmospheric Sci. 32:1975;233-242.
17. Kato T. Remarks on zero viscosity limit for nonstationary Navier Stokes flows with boundary. Seminar on Nonlinear Partial Differential Equations (Berkeley, CA, 1983). Math. Sci. Res. Inst. Publ. 2:1984;Springer-Verlag, New York/Berlin. p. 85-98.
18. Landau L., Lifchitz E. Mécanique des fluides. 1959;Mir.
19. Marsden J., Raţiu T. Nonlinear stability in fluids and plasmas. Seminar on New Results in Nonlinear Partial Differential Equations (Bonn, 1984). Aspects of Math. E10:1987;Vieweg, Brauschweig. p. 101-134.
20. Marchioro C., Pulvirenti M. Mathematical Theory of Incompressible Nonviscous Fluids. Applied Mathematical Sciences. 96:1994;Springer-Verlag.
21. Rayleigh Lord. On the stability, or instability, of certain fluid motions. Proc. London Math. Soc. 11:1880;57-70.
22. Schlichting H. Boundary Layer Theory. 1968;McGraw-Hill, New York.
23. Wang Temam. Asymptotic analysis of Oseen type equations in a channel at small viscosity. Indiana Univ. Math. J. 45:1996.