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

作     者：Xumin Gu Yu Mei 

作者机构：School of MathematicsShanghai University of Finance and EconomicsShanghai 200433China School of Mathematics and StatisticsNorthwestern Polytechnical UniversityXi'an 710129China 

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

年 卷 期：2023年第66卷第6期

页      面：1263-1300页

核心收录：

学科分类：080704[工学-流体机械及工程] 080103[工学-流体力学] 08[工学] 0807[工学-动力工程及工程热物理] 0801[工学-力学（可授工学、理学学位）] 

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) 

主　　题：free boundary viscoelastic fuid vanishing viscosity compressible fuid elastodynamics 

摘      要：We consider the free boundary problem of compressible isentropic neo-Hookean viscoelastic fluid equations with surface *** 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 *** 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 *** 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.