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Existence and regularity results for the primitive equations in two space dimensions. (English) Zbl 1060.35033
The aim of this article is to present various results of existence, uniqueness and regularity of solutions for the Primitive Equations of the ocean (PEs) in two space dimensions with periodic boundary conditions. First by recalling the variational formulation of the envisaged problem under suitable assumptions the existence of weak solutions for the PEs is proved. Then by deriving the necessary a priori estimates the authors also prove the existence and uniqueness of strong solutions and the existence of more regular solutions, up to $C^\infty$ regularity.

35B65Smoothness and regularity of solutions of PDE
35Q35PDEs in connection with fluid mechanics
35J20Second order elliptic equations, variational methods
86A05Hydrology, hydrography, oceanography
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