On the hydrostatic approximation of compressible anisotropic Navier–Stokes equations
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 small...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Académie des sciences
2021-08-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.186/ |
| Summary: | 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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| ISSN: | 1778-3569 |