Vanishing viscosity limits for the free boundary problem of compressible viscoelastic fluids with surface tension  

作　　者：Xumin Gu Yu Mei 

机构地区：[1]School of Mathematics,Shanghai University of Finance and Economics,Shanghai 200433,China [2]School of Mathematics and Statistics,Northwestern Polytechnical University,Xi'an 710129,China

出　　处：《Science China Mathematics》2023年第6期1263-1300,共38页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant No.12031006);the Shanghai Frontier Research Center of Modern Analysis;supported by National Natural Science Foundation of China (Grant No.12101496);the Fundamental Research Funds for the Central Universities (Grant No.G2021KY05101)。

摘　　要：We consider the free boundary problem of compressible isentropic neo-Hookean viscoelastic fluid equations with surface tension.Under the physical kinetic and dynamic conditions proposed on the free boundary,we investigate the regularity of classical solutions to viscoelastic fluid equations in Sobolev spaces which are uniform in viscosity and justify the corresponding vanishing viscosity limits.The key ingredient of our proof is that the deformation gradient tensor in Lagrangian coordinates can be represented as a parameter in terms of the flow map so that the inherent structure of the elastic term improves the uniform regularity of normal derivatives in the limit of vanishing viscosity.This result indicates that the boundary layer does not appear in the free boundary problem of compressible viscoelastic fluids,which is different from the case studied by Mei et al.(2018)for the free boundary compressible Navier-Stokes system.

关 键 词：free boundary viscoelastic fuid vanishing viscosity compressible fuid ELASTODYNAMICS 

分 类 号：O357[理学—流体力学]