Large friction limit of the compressible Navier-Stokes equations with Navier Boundary conditions in general three-dimensional domains

TL;DR

This paper proves that solutions of the compressible Navier-Stokes equations with Navier boundary conditions converge to those with no-slip conditions as the friction coefficient increases indefinitely, in three-dimensional domains.

Contribution

It establishes the large friction limit of the compressible Navier-Stokes equations with Navier boundary conditions in 3D domains, connecting two different boundary condition regimes.

Findings

Convergence of solutions as friction coefficient tends to infinity

Validation of boundary condition transition in compressible flows

Mathematical proof of the limit process

Abstract

In this paper, we study the Navier-Stokes equations of compressible, barotropic flow posed in a bounded set in $\mathbb{R}^3$ with different boundary conditions. Specifically, we prove that the local-in-time smooth solution of the Navier-Stokes equations with Navier boundary condition converges to the smooth solution of the Navier-Stokes equations with no-slip boundary condition as the Navier friction coefficient tends to infinity.