Journal
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
Volume 33, Issue 4, Pages 847-859Publisher
SIAM PUBLICATIONS
DOI: 10.1137/S0036141000375962
Keywords
Navier-Stokes equations; shallow domains; geophysical fluid dynamics; hydrostatic approximation; singular perturbation; compactness criterium; asymptotic analysis
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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.
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