Well-posedness for compressible Euler equations with physical vacuum singularity

Juhi Jang, Nader Masmoudi

Research output: Contribution to journalArticle

Abstract

An important problem in the theory of compressible gas flows is to understand the singular behavior of vacuum states. The main difficulty lies in the fact that the system becomes degenerate at the vacuum boundary, where the characteristic speeds u ± c coincide and have unbounded spatial derivative since c behaves like x1/2 close to the boundary. In this paper, we overcome this difficulty by presenting a new formulation and new energy spaces. We establish the local-in-time well-posedness of one-dimensional compressible Euler equations for isentropic flows with the physical vacuum singularity in some spaces adapted to the singularity.

Original languageEnglish (US)
Pages (from-to)1327-1385
Number of pages59
JournalCommunications on Pure and Applied Mathematics
Volume62
Issue number10
DOIs
StatePublished - Oct 2009

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Compressible Euler Equations
Euler equations
Well-posedness
Vacuum
Singularity
Compressible Flow
Gas Flow
Flow of gases
Derivatives
Derivative
Formulation
Energy

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Well-posedness for compressible Euler equations with physical vacuum singularity. / Jang, Juhi; Masmoudi, Nader.

In: Communications on Pure and Applied Mathematics, Vol. 62, No. 10, 10.2009, p. 1327-1385.

Research output: Contribution to journalArticle

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