[Sur l’approximation hydrostatique des équations de Navier–Stokes anisotropes compressibles]
Dans ce travail, nous obtenons l’approximation hydrostatique en prenant la limite du petit rapport d’aspect des équations de Navier–Stokes. Le rapport d’aspect (le rapport de la profondeur à la largeur horizontale) est une contrainte géométrique dans les mouvements géophysiques signifiant que l’échelle verticale est nettement plus petite que l’horizontale. Nous utilisons l’inégalité d’entropie relative pour prouver rigoureusement la limite des équations de Navier–Stokes compressibles aux équations primitives compressibles. C’est le premier travail qui utilise l’inégalité d’entropie relative pour prouver l’approximation hydrostatique et dériver les équations primitives compressibles.
In this work, we obtain the hydrostatic approximation by taking the small aspect ratio limit to the Navier–Stokes equations. The aspect ratio (the ratio of the depth to horizontal width) is a geometrical constraint in general large scale motions meaning that the vertical scale is significantly smaller than horizontal. We use the versatile relative entropy inequality to prove rigorously the limit from the compressible Navier–Stokes equations to the compressible Primitive Equations. This is the first work to use relative entropy inequality for proving hydrostatic approximation and derive the compressible Primitive Equations.
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@article{CRMATH_2021__359_6_639_0,
author = {Gao, Hongjun and Ne\v{c}asov\'a, \v{S}\'arka and Tang, Tong},
title = {On the hydrostatic approximation of compressible anisotropic {Navier{\textendash}Stokes} equations},
journal = {Comptes Rendus. Math\'ematique},
pages = {639--644},
publisher = {Acad\'emie des sciences, Paris},
volume = {359},
number = {6},
year = {2021},
doi = {10.5802/crmath.186},
language = {en},
url = {http://www.numdam.org/articles/10.5802/crmath.186/}
}
TY - JOUR AU - Gao, Hongjun AU - Nečasová, Šárka AU - Tang, Tong TI - On the hydrostatic approximation of compressible anisotropic Navier–Stokes equations JO - Comptes Rendus. Mathématique PY - 2021 SP - 639 EP - 644 VL - 359 IS - 6 PB - Académie des sciences, Paris UR - http://www.numdam.org/articles/10.5802/crmath.186/ DO - 10.5802/crmath.186 LA - en ID - CRMATH_2021__359_6_639_0 ER -
%0 Journal Article %A Gao, Hongjun %A Nečasová, Šárka %A Tang, Tong %T On the hydrostatic approximation of compressible anisotropic Navier–Stokes equations %J Comptes Rendus. Mathématique %D 2021 %P 639-644 %V 359 %N 6 %I Académie des sciences, Paris %U http://www.numdam.org/articles/10.5802/crmath.186/ %R 10.5802/crmath.186 %G en %F CRMATH_2021__359_6_639_0
Gao, Hongjun; Nečasová, Šárka; Tang, Tong. On the hydrostatic approximation of compressible anisotropic Navier–Stokes equations. Comptes Rendus. Mathématique, Tome 359 (2021) no. 6, pp. 639-644. doi : 10.5802/crmath.186. http://www.numdam.org/articles/10.5802/crmath.186/
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