Lagrangian formulation and a priori estimates for relativistic fluid flows with vacuum

Juhi Jang, Philippe G. LeFloch, Nader Masmoudi

Research output: Contribution to journalArticlepeer-review

Abstract

We study the evolution of a compressible fluid surrounded by vacuum and introduce a new symmetrization in Lagrangian coordinates that allows us to encompass both relativistic and non-relativistic fluid flows. The problem under consideration is a free boundary problem of central interest in compressible fluid dynamics and, from the mathematical standpoint, the main challenge to be overcome lies in the loss of regularity in the fluid variables near the free boundary. Based on our Lagrangian formulation, we establish the necessary a priori estimates in weighted Sobolev spaces which are adapted to this loss of regularity.

Original languageEnglish (US)
Pages (from-to)5481-5509
Number of pages29
JournalJournal of Differential Equations
Volume260
Issue number6
DOIs
StatePublished - Mar 15 2016

Keywords

  • Free boundary
  • Lagrangian formulation
  • Relativistic fluid
  • Vacuum state
  • Weighted energy

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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