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/ |
| _version_ | 1797651551841419264 |
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| author | Gao, Hongjun Nečasová, Šárka Tang, Tong |
| author_facet | Gao, Hongjun Nečasová, Šárka Tang, Tong |
| author_sort | Gao, Hongjun |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-11T16:16:26Z |
| format | Article |
| id | doaj.art-943df7fc96504185bdece68ff33d4a9a |
| institution | Directory Open Access Journal |
| issn | 1778-3569 |
| language | English |
| last_indexed | 2024-03-11T16:16:26Z |
| publishDate | 2021-08-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj.art-943df7fc96504185bdece68ff33d4a9a2023-10-24T14:19:22ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692021-08-01359663964410.5802/crmath.18610.5802/crmath.186On the hydrostatic approximation of compressible anisotropic Navier–Stokes equationsGao, Hongjun0Nečasová, Šárka1Tang, Tong2School of Mathematics, Southeast University, Nanjing 211189, P.R. ChinaInstitute of Mathematics, Žitná 25, 115 67 Praha 1, Czech RepublicSchool of Mathematical Science, Yangzhou University, Yangzhou 225002, P.R. ChinaIn 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.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.186/ |
| spellingShingle | Gao, Hongjun Nečasová, Šárka Tang, Tong On the hydrostatic approximation of compressible anisotropic Navier–Stokes equations Comptes Rendus. Mathématique |
| title | On the hydrostatic approximation of compressible anisotropic Navier–Stokes equations |
| title_full | On the hydrostatic approximation of compressible anisotropic Navier–Stokes equations |
| title_fullStr | On the hydrostatic approximation of compressible anisotropic Navier–Stokes equations |
| title_full_unstemmed | On the hydrostatic approximation of compressible anisotropic Navier–Stokes equations |
| title_short | On the hydrostatic approximation of compressible anisotropic Navier–Stokes equations |
| title_sort | on the hydrostatic approximation of compressible anisotropic navier stokes equations |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.186/ |
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