Well and ill-posedness for compressible Euler equations with vacuum

Juhi Jang, Nader Masmoudi

Research output: Contribution to journalArticle

Abstract

An interesting problem arising in gas and fluid dynamics is to understand the behavior of vacuum states, namely, the behavior of the system in the presence of vacuum. In this paper, we review and expand some local-in-time well-posedness results for one-dimensional compressible Euler equations for polytropic gases with a range of behaviors at the interface including the physical vacuum case. We also present some sort of ill-posedness results in some other cases. Finally, we present some conjectures about the change of behavior at the interface. This paper is a mixture of rigorous and formal calculations.

Original languageEnglish (US)
Article number115625
JournalJournal of Mathematical Physics
Volume53
Issue number11
DOIs
StatePublished - Nov 27 2012

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Compressible Euler Equations
Ill-posedness
Well-posedness
Vacuum
vacuum
gas dynamics
Gas Dynamics
fluid dynamics
Fluid Dynamics
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ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

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

In: Journal of Mathematical Physics, Vol. 53, No. 11, 115625, 27.11.2012.

Research output: Contribution to journalArticle

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