Asymptotic stability of strong contact discontinuity for full compressible Navier-Stokes equations with initial boundary value problem

TL;DR

This paper proves the asymptotic stability of strong contact discontinuities in the full compressible Navier-Stokes equations within a half-space, overcoming boundary decay challenges using energy methods.

Contribution

It establishes the stability of large, non-small contact discontinuities for the full compressible Navier-Stokes equations with boundary conditions, advancing understanding of boundary layer stability.

Findings

Proves asymptotic stability of strong contact discontinuities.

Handles large perturbations without smallness assumptions.

Uses elementary energy methods for proof.

Abstract

This paper is concerned with Dirichlet problem $u(0,t)=0$, $\theta(0,t)=\theta_-$ for one-dimensional full compressible Navier-Stokes equations in the half space $\R_+=(0,+\infty)$. Because the boundary decay rate is hard to control, stability of contact discontinuity result is very difficult. In this paper, we raise the decay rate and establish that for a certain class of large perturbation, the asymptotic stability result is contact discontinuity. Also, we ask the strength of contact discontinuity not small. The proofs are given by the elementary energy method.