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 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 GerardVaret(2019)and Wang et al.(2021));furthermore,the estimate of the pressure term in the hyperbolic Prandtl system gives rise to additional difficulties.
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)。
