Abstract
The initial boundary value problem for the two-dimensional primitive equations of largescale oceanic motion in geophysics is considered sequetially. Here the depth of the ocean is positive but not always a constant. By Faedo-Galerkin method and anisotropic inequalities, the existence and uniqueness of the global weakly strong solution and global strong solution for the problem are obtained. Moreover, by studying the asymptotic behavior of solutions for the above problem, the energy is exponential decay with time is proved.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bresch D, Kazhikhov A, Lemoine J. On the two-dimensional hydrostatic Navier-Stokes equations[J]. SIAM J Math Anal, 2004, 36(3):796–814.
Lions J L. Quelques méthodes de résolutions des problèmes aux limites nonlinéaires[M]. Paris: Dunod, 1969 (in French).
Guillén-González F, Masmoudi N, Rodríguez-Bellido M A. Anisotropic estimates and strong solutions for the primitive equations[J]. Diff Int Equ, 2001, 14(11):1381–1408.
Huang Daiwen, Guo Boling. On two-dimensional large-scale primitive equations in oceanic dynamics (I)[J]. Applied Mathematics and Mechanics (English Edition), 2007, 28(5):581–592.
Ziane M. Regularity results for the stationary primitive equations of the atmosphere and the ocean[J]. Nonlinear Anal, TMA, 1997, 28:289–313.
Author information
Authors and Affiliations
Corresponding author
Additional information
(Contributed by GUO Bo-ling)
Project supported by the National Natural Science Foundation of China (No.90511009)
Rights and permissions
About this article
Cite this article
Huang, Dw., Guo, Bl. On two-dimensional large-scale primitive equations in oceanic dynamics (II). Appl Math Mech 28, 593–600 (2007). https://doi.org/10.1007/s10483-007-0504-x
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/s10483-007-0504-x