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

2017/12/12 by Kreml, Ondřej, Nečasová, Šárka, Piasecki, Tomasz
#35Q30 #76N10 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1712.04568

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.

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