Asymptotic analysis of the primitive equations under the small depth assumption

Nonlinear Analysis, Theory, Methods and Applications

Volumn 61, Issue 3, 2005, Pages 425-460

  Hu, Changbing ^a  

^a TEXAS A AND M UNIVERSITY   (United States)

Author keywords

Asymptotic analysis; Primitive equations; Thin domains

Indexed keywords

APPROXIMATION THEORY; BOUNDARY CONDITIONS; MATHEMATICAL MODELS; METEOROLOGY; NAVIER STOKES EQUATIONS; PARTIAL DIFFERENTIAL EQUATIONS; THEOREM PROVING;

ASYMPTOTIC ANALYSIS; BAROCLINIC FLOW; PRIMITIVE EQUATIONS (PE); THIN DOMAINS;

NONLINEAR EQUATIONS;

EID: 14044278714     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2004.12.005     Document Type: Article

References (26)

1. J. Avrin Large eigenvalue existence and global regularity results for Navier-Stokes equations J. Differential Equations 127 1996 365 390
2. C. Foias, O. Manley, and R. Temam Modelling of the interaction of small and large eddies in two-dimensional turbulent flows RAIRO Modél. Math. Anal. Numér. 22 1 1988 93 118
3. J.K. Hale, and G. Raugel Reaction diffusion equations on thin domains J. Math. Pures Appl. 71 1992 33 95
4. J.K. Hale, and G. Raugel A damped hyperbolic equation on thin domains Trans. Amer. Math. Soc. 329 1992 185 219
5. G. Haltiner, and R. Williams Numerical Weather Prediction and Dynamic Meteorology second ed. 1980 Wiley New York
6. C. Hu, Finite dimensional behavior of the primitive equations under small depth assumption, preprint.
7. C. Hu, R. Temam, and M. Ziane Regularity results for GFD-Stokes problem and some related linear elliptic PDEs in primitive equations Chinese Ann. Math. 23B 2002 277 292
8. C. Hu, R. Temam, and M. Ziane The primitive equations on the large scale ocean under small depth hypothesis Discrete Contin. Dyn. System 9 2003 97 131
9. D. Iftimie, and G. Raugel Some results on the Navier-Stokes equations in thin 3D domain, Special issue in celebration of Jack K. Hale's 70th birthday, Part 4 (Atlanta, GA/Lisbon, 1998) J. Differential Equations 169 2001 281 331
10. O.A. Ladyzhenskaya The Mathematical Theory of Viscous Incompressible Flow second ed. 1969 Gordon and Breach New York
11. J.L. Lions, R. Temam, and S. Wang New formulation of the primitive equations of the atmosphere and applications Nonlinearity 5 1992 237 288
12. J.L. Lions, R. Temam, and S. Wang On the equations of the large scale ocean Nonlinearity 5 1992 1007 1053
13. J.L. Lions, R. Temam, and S. Wang Models of the coupled atmosphere and ocean (CAO I) Comput. Mech. Adv. 1 1993 5 54
14. I. Moise, R. Temam, and M. Ziane Asymptotic analysis of the Navier-Stokes equations in thin domains Topol. Methods Nonlinear Anal. 10 1997 249 282
15. J. Pedlosky, Geophysical Fluid Dynamics, second ed., Springer, New York.
16. G. Raugel, G. Sell, Navier-Stokes equations on thin 3D domains I: global regularity of spatially periodic conditions, College de France Proceedings, Pitman Research Notes on Mathematical Series, Pitman, New York, London, 1992.
17. G. Raugel, and G. Sell Navier-Stokes equations on thin 3D domains I global attractors and global regularity of solutions J. Amer. Math. Soc. 6 1993 503 568
18. E. Simonnet, T. Tachim Medjo, R. Temam, Higher order approximation equations for the primitive equations of the ocean, Proceedings of the Erice Conference, June 2003, to appear.
19. E. Simonnet, T. Tachim Medjo, R. Temam, On the order of magnitude of the baroclinic flow in the primitive equations of the ocean, Ann. Math. Pura Appl., 2004, to appear.
20. R. Temam, Infinite dimensional dynamical systems in Mechanics and Physics, Applied Mathematical Science, Vol. 68, second ed., Springer, New York, 1997.
21. R. Temam Navier-Stokes equations, Theory and Numerical Analysis, Reprint of the 1984 version 2001 AMS Chelsea Publishing Providence, RI
22. R. Temam, and M. Ziane Navier-Stokes equations in three dimensional thin domains with various boundary conditions Adv. Differential Equations 1 1996 499 546
23. R. Temam, M. Ziane, Navier-Stokes equations in thin spherical shells, Optim. Method. Partial Differential Equations, 1996, pp. 281-314, Contemp. Math. 209.
24. R. Temam, M. Ziane, Some mathematical problems in geophysical fluid dynamics, in: Handbook of Mathematical Fluid Dynamics, vol. 3, 2004, 535-657, North-Holland, Amsterdam.
25. W.M. Washington, and C.L. Parkinson Introduction to Three-Dimensional Climate Modeling 1986 Oxford University Press Oxford
26. M. Ziane Regularity results for Stokes type systems Appl. Anal. 58 1995 263 292