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An intrinsic analysis of existence of solutions for the hydrostatic approximation of Navier-Stokes equations. (English. Abridged French version) Zbl 0959.35134
Summary: We prove an existence result for the hydrostatic approximations of Navier-Stokes equations, also called primitive equations of the ocean. We perform a direct analysis of existence of solutions, which is not based upon a singular limit process. Our analysis is essentially based upon the existence of a reduced inf-sup condition for (3D) horizontal velocities and (2D) surface pressures. It applies to general domains, without the need of a boundary bank. Our existence result is, at the same time, a result of approximation by mixed finite elements.

MSC:
35Q30 Navier-Stokes equations
86A05 Hydrology, hydrography, oceanography
76M10 Finite element methods applied to problems in fluid mechanics
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