The strong inviscid limit of the isentropic compressible Navier-Stokes equations with Navier boundary conditions

TL;DR

This paper proves the existence and regularity of strong solutions to the 3D compressible Navier-Stokes equations with Navier boundary conditions, showing they converge to Euler solutions as viscosity vanishes.

Contribution

It establishes uniform-in-viscosity existence and regularity results for solutions on a half-space, and demonstrates their strong convergence to Euler solutions in the inviscid limit.

Findings

Existence of strong solutions with Navier boundary conditions

Uniform regularity independent of viscosity parameters

Strong convergence to Euler solutions as viscosity approaches zero

Abstract

We obtain existence and conormal Sobolev regularity of strong solutions to the 3D compressible isentropic Navier-Stokes system on the half-space with a Navier boundary condition, over a time that is uniform with respect to the viscosity parameters when these are small. These solutions then converge globally and strongly in $L^2$ towards the solution of the compressible isentropic Euler system when the viscosity parameters go to zero.