Uniform regularity and vanishing dissipation limit for the full compressible Navier-Stokes system in 3-D bounded domain

Abstract

In the present paper, we study the uniform regularity and vanishing dissipation limit for the full compressible Navier-Stokes system whose viscosity and heat conductivity are allowed to vanish at different order. The problem is studied in a 3-D bounded domain with Navier-slip type boundary conditions \eqref{1.9}. It is shown that there exists a unique strong solution to the full compressible Navier-Stokes system with the boundary conditions \eqref{1.9} in a finite time interval which is independent of the viscosity and heat conductivity. The solution is uniform bounded in $W^{1,\infty }$ and a conormal Sobolev space. Based on such uniform estimates, we prove the convergence of the solutions of the full compressible Navier-Stokes to the corresponding solutions of the full compressible Euler system in $L^{\infty }(0,T;L^2)$,$L^{\infty }(0,T;H^1)$ and $L^{\infty }([0,T]\times \Omega )$ with a rate of convergence.

49 pages

References in corpus (2)

• Uniform regularity and vanishing viscosity limit for the free surface Navier-Stokes equations
• Uniform regularity and vanishing viscosity limit for the compressible Navier-Stokes with general Navier-slip boundary conditions in 3-dimensional domains