Global hydrostatic approximation of the hyperbolic Navier-Stokes system with small Gevrey class 2 data In memory of Professor Geneviève Raugel

作     者：Marius Paicu Ping Zhang Marius Paicu;Ping Zhang

作者机构：Institut de Mathematiques de BordeauxUniversite BordeauxTalence 33405France Academy of Mathematics and Systems Science and Hua Loo-Keng Key Laboratory of MathematicsChinese Academy of SciencesBeijing 100190China School of Mathematical SciencesUniversity of Chinese Academy of SciencesBeijing 100049China 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2022年第65卷第6期

页      面：1109-1146页

核心收录：

学科分类：08[工学] 0801[工学-力学（可授工学、理学学位）] 

基　　金：supported by K.C.Wong Education Foundation supported by the Agence Nationale de la Recherche,Project IFSMACS(Interaction Fluide-Structure:Modélisation,analyse,contr?le et simulation)(Grant No.ANR-15-CE40-0010) supported by National Basic Research Program of China(Grant No.2021YFA1000800) National Natural Science Foundation of China(Grants Nos.11731007,12031006 and 11688101) 

主　　题：incompressible hyperbolic Navier-Stokes equations hydrostatic approximation hyperbolic Prandtl system 

摘      要：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 R×(0,ε).The formal limit of these equations is a hyperbolic Prandtl type *** first prove the global existence of solutions to these equations under a uniform smallness assumption on the data in the Gevrey class *** we justify the limit globally-in-time from the anisotropic hyperbolic Navier-Stokes system to the hyperbolic Prandtl system with such Gevrey class 2 *** 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 GerardVaret(2019)and Wang et al.(2021));furthermore,the estimate of the pressure term in the hyperbolic Prandtl system gives rise to additional difficulties.