Global hydrostatic approximation of the hyperbolic Navier-Stokes system with small Gevrey class 2 data

doi:10.1007/s11425-021-1956-8

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	Global hydrostatic approximation of the hyperbolic Navier-Stokes system with small Gevrey class 2 data
	Paicu, Marius 1; Zhang, Ping 2,3,4
	2022-03-31
Source Publication	SCIENCE CHINA-MATHEMATICS
ISSN	1674-7283
Pages	38
Abstract	We investigate the hydrostatic approximation of a hyperbolic version of Navier-Stokes equations, which is obtained by using the Cattaneo type law instead of the Fourier law, evolving in a thin strip Double-struck capital R x (0, epsilon). The formal limit of these equations is a hyperbolic Prandtl type equation. We first prove the global existence of solutions to these equations under a uniform smallness assumption on the data in the Gevrey class 2. Then we justify the limit globally-in-time from the anisotropic hyperbolic Navier-Stokes system to the hyperbolic Prandtl system with such Gevrey class 2 data. Compared with Paicu et al. (2020) for the hydrostatic approximation of the 2-D classical Navier-Stokes system with analytic data, here the initial data belongs to the Gevrey class 2, which is very sophisticated even for the well-posedness of the classical Prandtl system (see Dietert and Gerard-Varet (2019) and Wang et al. (2021)); furthermore, the estimate of the pressure term in the hyperbolic Prandtl system give rise to additional difficulties.
Keyword	incompressible hyperbolic Navier-Stokes equations hydrostatic approximation hyperbolic Prandtl system
DOI	10.1007/s11425-021-1956-8
Indexed By	SCI
Language	英语
Funding Project	K. C. Wong Education Foundation ; Agence Nationale de la Recherche[ANR-15-CE40-0010] ; National Key R&D Program of China[2021YFA1000800] ; National Natural Science Foundation of China[11731007] ; National Natural Science Foundation of China[12031006] ; National Natural Science Foundation of China[11688101]
WOS Research Area	Mathematics
WOS Subject	Mathematics, Applied ; Mathematics
WOS ID	WOS:000777869300001
Publisher	SCIENCE PRESS
Citation statistics
Document Type	期刊论文
Identifier	http://ir.amss.ac.cn/handle/2S8OKBNM/60279
Collection	中国科学院数学与系统科学研究院
Corresponding Author	Zhang, Ping
Affiliation	1.Univ Bordeaux, Inst Math Bordeaux, F-33405 Talence, France 2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 3.Chinese Acad Sci, Hua Loo Keng Key Lab Math, Beijing 100190, Peoples R China 4.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
Recommended Citation GB/T 7714	Paicu, Marius,Zhang, Ping. Global hydrostatic approximation of the hyperbolic Navier-Stokes system with small Gevrey class 2 data[J]. SCIENCE CHINA-MATHEMATICS,2022:38.
APA	Paicu, Marius,&Zhang, Ping.(2022).Global hydrostatic approximation of the hyperbolic Navier-Stokes system with small Gevrey class 2 data.SCIENCE CHINA-MATHEMATICS,38.
MLA	Paicu, Marius,et al."Global hydrostatic approximation of the hyperbolic Navier-Stokes system with small Gevrey class 2 data".SCIENCE CHINA-MATHEMATICS (2022):38.

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