Azérad, Pascal; Guillén, Francisco Mathematical justification of the hydrostatic approximation in the primitive equations of geophysical fluid dynamics. (English) Zbl 0999.35072 SIAM J. Math. Anal. 33, No. 4, 847-859 (2001). Summary: Geophysical fluids all exhibit a common feature: their aspect ratio (depth to horizontal width) is very small. This leads to an asymptotic model widely used in meteorology, oceanography, and limnology, namely the hydrostatic approximation of the time-dependent incompressible Navier-Stokes equations. It relies on the hypothesis that pressure increases linearly in the vertical direction. In the following, we prove a convergence and existence theorem for this model by means of anisotropic estimates and a new time-compactness criterium. Cited in 51 Documents MSC: 35Q30 Navier-Stokes equations 86A05 Hydrology, hydrography, oceanography 76D05 Navier-Stokes equations for incompressible viscous fluids Keywords:Navier-Stokes equations; shallow domains; geophysical fluid dynamics; hydrostatic approximation; singular perturbation; compactness criterium; asymptotic analysis PDFBibTeX XMLCite \textit{P. Azérad} and \textit{F. Guillén}, SIAM J. Math. Anal. 33, No. 4, 847--859 (2001; Zbl 0999.35072) Full Text: DOI