A priori estimates for relativistic liquid bodies

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We demonstrate that a sufficiently smooth solution of the relativistic Euler equations that represents a dynamical compact liquid body, when expressed in Lagrangian coordinates, determines a solution to a system of non-linear wave equations with acoustic boundary conditions. Using this wave formulation, we prove that these solutions satisfy energy estimates without loss of derivatives. Importantly, our wave formulation does not require the liquid to be irrotational, and the energy estimates do not rely on divergence and curl type estimates employed in previous works.

Original languageEnglish
Pages (from-to)105-222
Number of pages118
JournalBulletin des Sciences Mathematiques
Issue number3
Publication statusPublished - 1 May 2017


  • A priori estimates
  • Acoustic boundary conditions
  • Relativistic Euler equations
  • Relativistic fluid bodies

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