On the inviscid limit of the compressible Navier-Stokes equations near Onsager's regularity in bounded domains

作     者：Robin Ming Chen Zhilei Liang Dehua Wang Runzhang Xu 

作者机构：Department of MathematicsUniversity of PittsburghPittsburghPA 15260USA School of MathematicsSouthwestern University of Finance and EconomicsChengdu 611130China College of Mathematical SciencesHarbin Engineering UniversityHarbin 150001China 

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

年 卷 期：2024年第67卷第1期

页      面：1-22页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by National Science Foundation of USA(Grant No.DMS-1907584) supported by the Fundamental Research Funds for the Central Universities(Grant No.JBK 2202045) supported by National Science Foundation of USA(Grant Nos.DMS-1907519 and DMS-2219384) supported by National Natural Science Foundation of China(Grant No.12271122) 

主　　题：inviscid limit Navier-Stokes equations Euler equations weak solutions bounded domain Katotype criterion Onsager’s regularity 

摘      要：The viscous dissipation limit of weak solutions is considered for the Navier-Stokes equations of compressible isentropic flows confined in a bounded *** establish a Kato-type criterion for the validity of the inviscid limit for the weak solutions of the Navier-Stokes equations in a function space with the regularity index close to Onsager’s critical *** particular,we prove that under such a regularity assumption,if the viscous energy dissipation rate vanishes in a boundary layer of thickness in the order of the viscosity,then the weak solutions of the Navier-Stokes equations converge to a weak admissible solution of the Euler *** approach is based on the commutator estimates and a subtle foliation technique near the boundary of the domain.