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On the hydrostatic approximation of compressible anisotropic Navier-Stokes equations
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SYSNO ASEP 0545358 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title On the hydrostatic approximation of compressible anisotropic Navier-Stokes equations Author(s) Gao, H. (CN)
Nečasová, Šárka (MU-W) RID, SAI, ORCID
Tang, T. (CN)Source Title Comptes Rendus Mathematique. - : Elsevier - ISSN 1631-073X
Roč. 359, č. 6 (2021), s. 639-644Number of pages 6 s. Language eng - English Country FR - France Keywords primitive equations ; weak solutins ; justificatio atmosphere Subject RIV BA - General Mathematics OECD category Pure mathematics R&D Projects GA19-04243S GA ČR - Czech Science Foundation (CSF) Method of publishing Open access Institutional support MU-W - RVO:67985840 UT WOS 000689678100001 EID SCOPUS 85114134897 DOI 10.5802/crmath.186 Annotation 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. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2022 Electronic address https://doi.org/10.5802/crmath.186
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