Abstract
The initial boundary value problem for the two-dimensional primitive equations of large scale oceanic motion in geophysics is considered. It is assumed that the depth of the ocean is a positive constant. Firstly, if the initial data are square integrable, then by Fadeo-Galerkin method, the existence of the global weak solutions for the problem is obtained. Secondly, if the initial data and their vertical derivatives are all square integrable, then by Faedo-Galerkin method and anisotropic inequalities, the existerce and uniqueness of the global weakly strong solution for the above initial boundary problem are obtained.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Lions J L, Teman R, Wang S. New formulations of the primitive equations of atmosphere and applications[J]. Nonlinearity, 1992, 5:237–288.
Lions J L, Teman R, Wang S. On the equations of the large scale ocean[J]. Nonlinearity, 1992, 5:1007–1053.
Lions J L, Teman R, Wang S. Models of the coupled atmosphere and ocean(CAO I)[J]. Computational Mechanics Advance, 1993, 1:1–54.
Lions J L, Teman R, Wang S. Mathematical theory for the coupled atmosphere-ocean models(CAO III)[J]. J Math Pures Appl, 1995, 74:105–163.
Wang S. On the 2D model of large scale atmosphic motion: well-posedness and attractors[J]. Nonlinear Anal, TMA, 1992, 18:17–60.
Bresch D, Guillén-González F, Masmoudi N, Rodríguez-Bellido M A. On the uniqueness for the two-dimensional primitive equations[J]. Diff Int Equ, 2003, 16(1):77–94.
Bresch D, Kazhikhov A, Lemoine J. On the two-dimensional hydrostatic Navier-Stokes equations[J]. SIAM J Math Anal, 2004, 36(3):796–814.
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.
Petcu M, Temam R, Wirosoetisno D. Existence and regularity results for the primitive equations in the two dimensions[J]. Comm on Pure and Appl Anal, 2004, 3(1):115–131.
Huang Daiwen, Guo Bolingl. On two-dimensional primitive equations of large scale ocean in oceanic dynamics (II)[J]. Applied Mathematics and Mechanics (English Edition), 2007, 28(5):593–600.
Pedlosky J. Geophysical fluid dynamics[M]. 2nd Ed. Berlin/New York: Springer-Verlag, 1987.
Washington W M, Parkinson C L. An introduction to three-dimensional climate modelling[M]. England: Oxford Univ Press, 1986.
Lions J L. Quelques méthodes de résolutions des problèmes aux limites nonlinéaires[M]. Paris: Dunod, 1969 (in French).
Teman R. Infinite-dimensional dynamical systems in mechanics and physics[M]. 2nd Ed, Appl Math Ser, Vol 68, Berlin: Springer-Verlag, 1997.
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 (I). Appl Math Mech 28, 581–592 (2007). https://doi.org/10.1007/s10483-007-0503-x
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/s10483-007-0503-x