On the derivation of homogeneous hydrostatic equations

Mathematical Modelling and Numerical Analysis

Volumn 33, Issue 5, 1999, Pages 965-970

  Grenier, Emmanuel ^a  

^a UNITÉ DE MATHÉMATIQUES PURES ET APPLIQUÉES   (France)

Author keywords

Shear flow; Stability

Indexed keywords

EID: 0033454916     PISSN: 0764583X     EISSN: None     Source Type: Journal    
DOI: 10.1051/m2an:1999128     Document Type: Article

References (10)

1. V.I. Arnold, Sur la géométrie différentielle des groupes de Lie de dimension infinie et ses applications à l'hydrodynamique des fluides parfaits. Ann. Inst. Fourier 16 (1996) 319-361.
2. Y. Brenier, Homogeneous hydrostatic flows with convex velocity profiles. Nonlinearity 12 (1999) 495-512.
3. Y. Brenier, Comparaison du régime hydrostatique des fluides incompressibles non visqueux et du régime quasineutre des plasmas. Private communication (1998).
4. B. Desjardins, E. Dormy and E. Grenier, Reynolds.m, a matlab package to compute Reynolds numbers of shear layers. Preprint and package, available at http://www.dmi.ens.fr/equipes/edp/reynolds.html.
5. S. Friedlander, W. Strauss and M. Vishik, Nonlinear instability in an ideal fluid. Ann. Inst. H. Poincaré. Anal. Non Linéaire 14 (1997) 187-209.
6. E. Grenier, On the stability of boundary layers of incompressible Euler equations. J. Differential Equations (to appear).
7. E. Grenier, Boundary layers of 2D inviscid fluids from an Hamiltonian viewpoint. Math. Res. Lett. 6 (1999) 1-13.
8. E. Grenier, On the nonlinear instability of Euler and Navier-Stokes equations (in preparation).
9. P.-L. Lions, Mathematical topics in fluid Mechanics, Vol 1, Incompressible models, in Oxford Lecture Series in Mathematics and its Applications, 3. Oxford Science Publications, The Clarendon Press, Oxford University Press, New York (1996).
10. Lord Rayleigh, On the stability, or instability, of certain fluid motions. Proc. London Math. Soc. 11 (1880) 57-70.