ON THE 3D VISCOUS PRIMITIVE EQUATIONS OF THE LARGE-SCALE ATMOSPHERE

doi:10.1016/S0252-9602(09)60074-6

数学物理学报(英文版) ›› 2009, Vol. 29 ›› Issue (4): 846-866.doi: 10.1016/S0252-9602(09)60074-6

ON THE 3D VISCOUS PRIMITIVE EQUATIONS OF THE LARGE-SCALE ATMOSPHERE

1.Institute of Applied Physics and Computational Mathematics, Beijing 100088, China；2.Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China

收稿日期:2008-12-31 出版日期:2009-07-20 发布日期:2009-07-20
基金资助:
The work was supported in part by the NSF of China (90511009, 10801017) and National Basic Research Program of China (973 Program, 2007CB814800)

ON THE 3D VISCOUS PRIMITIVE EQUATIONS OF THE LARGE-SCALE ATMOSPHERE

1.Institute of Applied Physics and Computational Mathematics, Beijing 100088, China；2.Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China

Received:2008-12-31 Online:2009-07-20 Published:2009-07-20
Supported by:
The work was supported in part by the NSF of China (90511009, 10801017) and National Basic Research Program of China (973 Program, 2007CB814800)

摘要/Abstract

摘要：

This paper is devoted to considering the three-dimensional viscous primitive equations of the large-scale atmosphere. First, we prove the global well-posedness for the primitive equations with weaker initial data than that in [11]. Second, we obtain the existence of smooth solutions to the equations. Moreover, we obtain the compact global attractor in V for the dynamical system generated by the primitive equations of large-scale
atmosphere, which improves the result of [11].

关键词: primitive equations, Navier-Stokes equations, global well-posedness, smooth solutions

Abstract:

Key words: primitive equations, Navier-Stokes equations, global well-posedness, smooth solutions

中图分类号:

35Q30

郭柏灵, 黄代文. ON THE 3D VISCOUS PRIMITIVE EQUATIONS OF THE LARGE-SCALE ATMOSPHERE[J]. 数学物理学报(英文版), 2009, 29(4): 846-866.

GUO Bai-Ling, HUANG Dai-Wen. ON THE 3D VISCOUS PRIMITIVE EQUATIONS OF THE LARGE-SCALE ATMOSPHERE[J]. Acta mathematica scientia,Series B, 2009, 29(4): 846-866.

参考文献

[1] Bourgeois A J, Beale J T. Validity of the quasigeostrophic model for large-scale flow in the atmosphere
and ocean. SIAM J Math Anal, 1994, 25: 1023-1068

[2] Cordoba D. Nonexistence of simple hyperbolic blow-up for the quasi-geostrophic equation. Ann Math,
1998, 148: 1135-1152

[3] Charve F. Global well posedness and asymptotics for a geophysical fluid system. Comm in PDE, 2004,
29: 1919-1940

[4] Constantin P, Majda A, Tabak E. Formation of strong fronts in the 2-D quasigeostrophic thermal active
scalar. Nonlinearity, 1994, 7: 1495-1533

[5] Constantin P, Majda A, Tabak E. Singular front formation in a model for quasigeostrophic flow. Phys
Fluids, 1994, 6: 9-11

[6] Cao C, Titi E S. Global well-posedness and finite dimensional global attractor for a 3-D planetary
geostrophic viscous model. Comm Pure Appl Math, 2003, 56: 198-133

[7] Cao C, Titi E S, Ziane M. A 揾orizontal?hyper-diffusion 3-D thermocline planetary geostrophic model:
well-posedness and long-time behavior. Nonlinearity, 2004, 17: 1749-1776

[8] Cao C, Titi E S. Global well-posedness of the three-dimensional viscous primitive equations of large-scale
ocean and atmosphere dynamics. Ann Math, 2007, 166: 245?67

[9] Constantin P, Wu J. Behavior of solutions of 2D quasi-geostrophic equations. SIAM J Math Anal, 1999,
30: 937?48

[10] Embid P F, Majda A J. Averaging over fast gravity waves for geophysical flows with arbitrary potential
vorticity. Comm in PDE, 1996, 21: 619-658

[11] Huang D, Guo B. On the existence of atmospheric attractors. Sci in China, Ser D: Earth Sciences, 2008,
51(3): 469?80

[12] Guo B, Huang D. Existence of weak solutions and trajectory attractors for the moist atmospheric equations
in geophysics. J Math Phys, 2006, 47: 083508

[13] Guill磂n-Gonz碼lez F, Masmoudi N, Rodr待guez-Bellido M A. Anisotropic estimates and strong solutions for
the primitive equations. Diff Int Equ, 2001, 14: 1381-1408

[14] Hu C, Temam R, Ziane M. The primimitive equations of the large scale ocean under the small depth
hypothesis. Disc and Cont Dyn Sys, 2003, 9(1): 97-131

[15] Lions J L. Quelques Méthodes De résolutions Des problèmes Aux Limites Nonlinéaires. Paris: Dunod,
1969

[16] Lions J L, Temam R, Wang S. New formulations of the primitive equations of atmosphere and applications.
Nonlinearity, 1992, 5: 237-288

[17] Lions J L, Temam R, Wang S. Models of the coupled atmosphere and ocean (CAO I). Computational
Mechanics Advance, 1993, 1: 1-4

[18] Lions J L, Temam R, Wang S. On the equations of the large scale ocean. Nonlinearity, 1992, 5: 1007-1053

[19] Majda A. Introduction to PDEs and Waves for the Atmosphere and Ocean. Courant Lecture Notes in
Mathematics, 9. Amer Math Soc, 2003

[20] Pedlosky J. Geophysical Fluid Dynamics. 2nd ed. Berlin, New York: Springer-Verlag, 1987

[21] Simonnet E, Tachim Medjo T, Temam R. Barotropic-baroclinic formulation of the primitive equations for
the ocean. Appl Anal, 2003, 82(5): 439-456

[22] Temam R. Infinite-Dimensional Dynamical Systems in Mechanics and Physics. 2nd ed. Appl Math Ser,
Vol 68. New York: Springer-Verlag, 1997

[23] Temam R, Ziane M. Some mathematical problems in geophysical fluid dynamics//Handbook of Mathe-
matical Fluid Dynamics, 3. Amsterdam: Elsevier, 2005: 535-258

ON THE 3D VISCOUS PRIMITIVE EQUATIONS OF THE LARGE-SCALE ATMOSPHERE

ON THE 3D VISCOUS PRIMITIVE EQUATIONS OF THE LARGE-SCALE ATMOSPHERE

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