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

Part of: Compressible fluids and gas dynamics, general Equations of mathematical physics and other areas of application

Published online by Cambridge University Press:  01 April 2019

Ondřej Kreml ,
Šárka Nečasová  and
Tomasz Piasecki
Ondřej Kreml
Affiliation:
Institute of Mathematics, Czech Academy of Sciences, Žitná 25, 115 67 Praha, Czech Republic (kreml@math.cas.cz; matus@math.cas.cz)
Šárka Nečasová
Affiliation:
Institute of Mathematics, Czech Academy of Sciences, Žitná 25, 115 67 Praha, Czech Republic (kreml@math.cas.cz; matus@math.cas.cz)
Tomasz Piasecki
Affiliation:
Institute of Applied Mathematics and Mechanics, University of Warsaw, Banacha 2, 02-097, Warszawa, Poland (tpiasecki@mimuw.edu.pl)
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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.

Keywords

compressible Navier–Stokes equationstime-dependent domainstrong solutionlocal existenceweak–strong uniqueness

MSC classification

Primary: 35Q30: Navier-Stokes equations
Secondary: 76N10: Existence, uniqueness, and regularity theory
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 150 , Issue 5 , October 2020 , pp. 2255 - 2300
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Copyright
Copyright © Royal Society of Edinburgh 2019

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