Local existence of strong solutions and weak-strong uniqueness for the compressible Navier-Stokes system on moving domains

TL;DR

This paper establishes local-in-time existence of strong solutions and proves weak-strong uniqueness for the compressible Navier-Stokes system on moving domains with various boundary conditions, using domain transformation techniques.

Contribution

It provides the first proof of weak-strong uniqueness for slip boundary conditions in the context of moving domains.

Findings

Proved local existence of strong solutions for both no-slip and slip boundary conditions.

Established weak-strong uniqueness principle for slip boundary conditions.

Applied transformation to fixed domain to handle moving boundary problems.

Abstract

We consider the compressible Navier-Stokes system on time-dependent domains with prescribed motion of the boundary. For both the no-slip boundary conditions as well as slip boundary conditions we prove local-in-time existence of strong solutions. These results are obtained using a transformation of the problem to a fixed domain and an existence theorem for Navier-Stokes like systems with lower order terms and perturbed boundary conditions. We also show the weak-strong uniqueness principle for slip boundary conditions which remained so far open question.