On mathematical problems for the primitive equations of the ocean: The mesoscale midlatitude case

Nonlinear Analysis, Theory, Methods and Applications

Volumn 40, Issue 1, 2000, Pages 439-482

  Lions, Jacques L ^a   Temam, Roger ^b,c   Wang, Shouhong ^b  

^a Centre de Recherche Interdisciplinaire en Biologie   (France)

^b INDIANA UNIVERSITY   (United States)

^c UNIVERSITÉ PARIS SACLAY   (France)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; BOUNDARY CONDITIONS; MATHEMATICAL MODELS; MATHEMATICAL TRANSFORMATIONS; PROBLEM SOLVING; THEOREM PROVING; VECTORS;

BOUSSINESQ EQUATION; GEOSTROPHIC ASYMPTOTICS; MESOSCALE MIDLATITUDE CASE; PRIMITIVE EQUATIONS; QUASI-GEOSTROPHIC (QG) EQUATIONS;

EQUATIONS OF MOTION;

EID: 0034172716     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(00)85026-9     Document Type: Article

References (23)

1. A. Babin, A. Mahalov, B. Nicholaenko, Global splitting, integrability and regularity of 3D Euler and Navier-Stokes equations for uniformly rotating fluids. Asymptotic Anal. 15 (1997) 103-150.
2. A.J. Bourgeois, J.T. Beale, Validity of the quasigeostrophic model for large-scale flow in the atmosphere and the ocean, SIAM J. Math. Anal. 25 (4) (1994) 1023-1068.
3. J.Y. Chemin, A propos d'un problème de pénalisation de type antisymétrique, C. R. Acad. Sci. Paris Sér. I Math. 321 (7) (1995) 861-864.
4. P.F. Embid, A. Majda, Averaging over fast gravity waves for geophysical flows with arbitrary potential vorticity, Comm. PDE 21 (1996) 619-658.
5. I. Gallager, Un résultat de stabilité pour les équations des fluides tournants. C. R. Acad. Sci. Paris Serie I 324 (1997) 183-186.
6. M. Ghil, S. Childress, Topics in Geophysical Fluid Dynamics: Atmospheric Dynamics. Dynamo Theory, and Climate Dynamics, Springer, New York, 1987.
7. E. Grenier, Couches limites de systèmes paraboliques nonlinéaires caractéristiques. Comptes Rendus Acad. Sci. Paris 323 (9) (1996) 1013-1017.
8. B. Legras, M. Ghil, Persistant anomalies, blocking and variations in atmosphere predictability, J. Atmospheric. Sci. 42 (1985) 433-471.
9. J. Leray, Essai sur le mouvement plan d'un liquide visqueux que limitent des parois, J. Math. Pures et Appl. 13 (1934) 331-418.
10. J. Leray, Sur le mouvement d'un liquide visqueux emplissant l'espace, Acta Math. 63 (1934) 193-248.
11. J.L. Lions, Quelques Méthodes de Résolution des Problèmes aux Limites Nonlinéaires, Dunod, Paris, 1969.
12. J.L. Lions, R. Temam, S. Wang, New formulations of the primitive equations of the atmosphere and applications, Nonlinearity 5 (1992) 237-288.
13. J.L. Lions, R. Temam, S. Wang, On the Equations of Large-Scale Ocean, Nonlinearity 5 (1992) 1007-1053.
14. J.L. Lions, R. Temam, S. Wang, Models of the coupled atmosphere and ocean (CAO I). Comput. Mech. Adv. 1 (1993) 3-54.
15. J.L. Lions, R. Temam, S. Wang, Geostrophic asymptotics of the primitive equations of the atmosphere, Topological Meth. Nonlinear Anal. 4 (1994) 253-287.
16. J.L. Lions, R. Temam, S. Wang, A Simple Global Model for the General Circulation of the Atmosphere, Dedicated to Peter D. Lax and Louis Nirenberg on the occasion of their 70th birthdays, Comm. Pure. Appl. Math. 50 (8) (1997) 707-752.
17. J. Pedlosky, Geophysical Fluid Dynamics, 2nd Edition, Springer, New York, 1987.
18. J.P. Peixoto, A.H. Oort, Physics of Climate, American Institute of Physics, New-York, 1992.
19. N.A. Phillips, Geostrophic motion. Rev. Geophys. 1 (1963) 123-176.
20. R. Temam, Navier-Stokes Equations: Theory and Numerical Analysis, North-Holland, Amsterdam, 1984.
21. S. Wang, On solvability for the equations of the large-scale atmospheric motion, Ph.D. Thesis, Lanzhou University. China, 1988.
22. S. Wang, Attractors for the 3D baroclinic quasi-geostrophic equations of large scale atmosphere, J. Math. Anal. Appl. 165 (1992) 266-283.
23. W.M. Washington, C.L. Parkinson, An Introduction to Three-Dimensional Climate Modeling, Oxford University Press, Oxford, 1986.