On the hydrostatic approximation of compressible anisotropic Navier-Stokes equations

0545358 - MÚ 2022 RIV FR eng J - Journal Article
Gao, H. - Nečasová, Šárka - Tang, T.
On the hydrostatic approximation of compressible anisotropic Navier-Stokes equations.
Comptes Rendus Mathematique. Roč. 359, č. 6 (2021), s. 639-644. ISSN 1631-073X. E-ISSN 1778-3569
R&D Projects: GA ČR(CZ) GA19-04243S
Institutional support: RVO:67985840
Keywords : primitive equations * weak solutins * justificatio atmosphere
OECD category: Pure mathematics
Impact factor: 0.773, year: 2021
Method of publishing: Open access
https://doi.org/10.5802/crmath.186

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.
Permanent Link: http://hdl.handle.net/11104/0322068