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

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

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The viscous dissipation limit of weak solutions is considered for the Navier-Stokes equations of compressible isentropic flows confined in a bounded domain.We 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 threshold.In 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 equations.Our approach is based on the commutator estimates and a subtle foliation technique near the boundary of the domain.

inviscid limitNavier-Stokes equationsEuler equationsweak solutionsbounded domainKato-type criterionOnsager's regularity

Robin Ming Chen、Zhilei Liang、Dehua Wang、Runzhang Xu

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Department of Mathematics,University of Pittsburgh,Pittsburgh,PA 15260,USA

School of Mathematics,Southwestern University of Finance and Economics,Chengdu 611130,China

College of Mathematical Sciences,Harbin Engineering University,Harbin 150001,China

National Science Foundation of USAFundamental Research Funds for the Central UniversitiesNational Science Foundation of USANational Science Foundation of USANational Natural Science Foundation of China

DMS-1907584JBK 2202045DMS-1907519DMS-221938412271122

2024

10.1007/s11425-022-2085-3

中国科学:数学(英文版)
中国科学院

中国科学:数学(英文版)

CSTPCD
影响因子：0.36
ISSN：1674-7283
年,卷(期)：2024.67(1)
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