Global well-posedness and asymptotics for a geophysical fluid system

Communications in Partial Differential Equations

Volumn 29, Issue 11-12, 2004, Pages 1919-1940

  Charve, Frédéric ^a  

^a ECOLE POLYTECHNIQUE   (France)

Author keywords

Anisotropy; Primitive system; Quasigeostrophic system; Strichartz inequalities

Indexed keywords

EID: 10844292502     PISSN: 03605302     EISSN: None     Source Type: Journal    
DOI: 10.1081/PDE-200043510     Document Type: Review

References (18)

1. Babin, A., Mahalov, A., Nicolaenko, B. (1997). On the asymptotic regimes and the strongly stratified limit of rotating Boussinesq equations. J. Theor. Comp. Fluid Dyn. 9:223-251.
2. Babin, A., Mahalov, A., Nicolaenko, B. (2001). Strongly stratified limit of 3D primitive equations in an infinite layer. Contem. Math. 283:1-11.
3. Bougeault, P., Sadourny, R. (2001). Dynamique de l'atmosphère et de l'océan. Editions de l'Ecole Polytechnique.
4. Charve, F. (2003). Convergence de solutions faibles du système primitif des équations quasigéostrophiques, accepted in Asymptotic Analysis.
5. Chemin, J.-Y., (1992). Remarques sur l'existence globale pour le système de Navier-Stokes incompressible. SIAM J. Math. Anal. 23:20-28.
6. Chemin, J.-Y. (1997). A propos d'un problème de pénalisation de type antisymétrique. Journal de Mathématiques Pures et Appliquées 76:739-755.
7. Chemin, J.-Y., Desjardins, B., Gallagher, I., Grenier, E. (2002). Anisotropy and dispersion in rotating fluids, nonlinear partial differential equations and their applications. Collège de France Seminar, Stud. Math. Appl. 31:171-191. (In French: Anisotropie et dispersion dans les fluides tournants, Compres-Rendus de l'Académie des Sciences (CRAS) 329, Série I, 1055-1058, 1999.)
8. Chemin, J.-Y., Desjardins, B., Gallagher, I., Grenier, E. (2002). Anisotropy and dispersion in rotating fluids, nonlinear partial differential equations and their applications. Collège de France Seminar, Stud. Math. Appl. 31:171-191. (In French: Anisotropie et dispersion dans les fluides tournants, Compres-Rendus de l'Académie des Sciences (CRAS) 329, Série I, 1055-1058, 1999.)
9. Cushman-Roisin, B. (1994). Introduction to Geophysical Fluid Dynamics. Prentice-Hall.
10. Embid, P., Majda, A. (1996). Averaging over fast gravity waves for geophysical flows with arbitrary potential vorticity. Commun. Partial Differential Equations 21:619-658.
11. Fujita, H., Kato, T. (1964). On the Navier-Stokes initial value problem I. Archiv Rationnal Mech. Anal. 16:269-315.
12. Gallagher, I. (1998). Applications of Schochet's methods to parabolic equations. Journal de Mathématiques Pures et Appliquées 77:989-1054.
13. Gill, A. (1982). Atmosphere-Ocean Dynamics. International Geophysics Series. Vol. 30. Academic Press.
14. Ginibre, J., Velo, G. (1995). Generalized Strichartz inequalities for the wave equations. J. Funct. Anal. 133:50-68.
15. Greenspan, H.-P. (1969). The Theory of Rotating Fluids. Cambridge Monographs on Mechanics and Applied Mathematics. Cambridge University Press.
16. Leray, J. (1933). Essai sur le mouvement d'un liquide visqueux emplissant l'espace. Acta Mathematica 63:193-248.
17. Lions, J.-L., Temam, R., Wang, S. (1994). Geostrophic asymptotics of the primitive equations of the atmosphere. Topological Methods Non Linear Anal. 4:1-35.
18. Pedlosky, J. (1979). Geophysical Fluid Dynamics. Springer.