On the hydrostatic approximation of compressible anisotropic Navier-Stokes equations

0545358 - MÚ 2022 RIV FR eng J - Článek v odborném periodiku
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
Grant CEP: GA ČR(CZ) GA19-04243S
Institucionální podpora: RVO:67985840
Klíčová slova: primitive equations * weak solutins * justificatio atmosphere
Obor OECD: Pure mathematics
Impakt faktor: 0.773, rok: 2021
Způsob publikování: 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.
Trvalý link: http://hdl.handle.net/11104/0322068