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 in...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.展开更多
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)+1 种基金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)。
文摘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.
