Chacón Rebollo, Tomás; Guillén González, Francisco An intrinsic analysis of existence of solutions for the hydrostatic approximation of Navier-Stokes equations. (English. Abridged French version) Zbl 0959.35134 C. R. Acad. Sci., Paris, Sér. I, Math. 330, No. 9, 841-846 (2000). 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. Cited in 18 Documents MSC: 35Q30 Navier-Stokes equations 86A05 Hydrology, hydrography, oceanography 76M10 Finite element methods applied to problems in fluid mechanics Keywords:mixed finite elements; hydrostatic approximations; Navier-Stokes equations; primitive equations of the ocean PDFBibTeX XMLCite \textit{T. Chacón Rebollo} and \textit{F. Guillén González}, C. R. Acad. Sci., Paris, Sér. I, Math. 330, No. 9, 841--846 (2000; Zbl 0959.35134) Full Text: DOI