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Mathematical justification of the hydrostatic approximation in the primitive equations of geophysical fluid dynamics

 

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Opened Access Mathematical justification of the hydrostatic approximation in the primitive equations of geophysical fluid dynamics
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Author: Azérad, Pascal
Guillén González, Francisco Manuel
Department: Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico
Date: 2001
Published in: SIAM Journal on Mathematical Analysis, 33(4), 847-859
Document type: Article
Abstract: 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.
Cite: Azérad, P. y Guillén González, F.M. (2001). Mathematical justification of the hydrostatic approximation in the primitive equations of geophysical fluid dynamics. SIAM Journal on Mathematical Analysis, 33 (4), 847-859.
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URI: http://hdl.handle.net/11441/41261

DOI: 10.1137/S0036141000375962

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