Well-posedness of compressible euler equations in a physical vacuum

Juhi Jang, Nader Masmoudi

Research output: Contribution to journalArticlepeer-review

Abstract

An important problem in gas and fluid dynamics is to understand the behavior of vacuum states, namely the behavior of the system in the presence of a vacuum. In particular, physical vacuum, in which the boundary moves with a nontrivial finite normal acceleration, naturally arises in the study of the motion of gaseous stars or shallow water. Despite its importance, there are only a few mathematical results available near a vacuum. The main difficulty lies in the fact that the physical systems become degenerate along the vacuum boundary. In this paper, we establish the local-in-time well-posedness of three-dimensional compressible Euler equations for polytropic gases with a physical vacuum by considering the problem as a free boundary problem.

Original languageEnglish (US)
Pages (from-to)61-111
Number of pages51
JournalCommunications on Pure and Applied Mathematics
Volume68
Issue number1
DOIs
StatePublished - Jan 1 2015

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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