Weak-strong uniqueness for the isentropic compressible navier-stokes system

Research output: Contribution to journalArticle

Abstract

We prove weak-strong uniqueness results for the isentropic compressible Navier-Stokes system on the torus. In other words, we give conditions on a weak solution, such as the ones built up by Lions (Compressible Models, Oxford Science, Oxford, 1998), so that it is unique. It is of fundamental importance since uniqueness of these solutions is not known in general. We present two different methods, one using relative entropy, the other one using an improved Gronwall inequality due to the author; these two approaches yield complementary results. Known weak-strong uniqueness results are improved and classical uniqueness results for this equation follow naturally.

Original languageEnglish (US)
Pages (from-to)137-146
Number of pages10
JournalJournal of Mathematical Fluid Mechanics
Volume13
Issue number1
DOIs
StatePublished - Mar 2011

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Navier-Stokes System
uniqueness
Entropy
Uniqueness
Gronwall Inequality
Relative Entropy
Uniqueness of Solutions
Weak Solution
Torus
entropy
Model

ASJC Scopus subject areas

  • Applied Mathematics
  • Mathematical Physics
  • Computational Mathematics
  • Condensed Matter Physics

Cite this

Weak-strong uniqueness for the isentropic compressible navier-stokes system. / Germain, Pierre.

In: Journal of Mathematical Fluid Mechanics, Vol. 13, No. 1, 03.2011, p. 137-146.

Research output: Contribution to journalArticle

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