Abstract
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 language | English |
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Pages (from-to) | 105-222 |
Number of pages | 118 |
Journal | Bulletin des Sciences Mathematiques |
Volume | 141 |
Issue number | 3 |
DOIs | |
Publication status | Published - 1 May 2017 |
Keywords
- A priori estimates
- Acoustic boundary conditions
- Relativistic Euler equations
- Relativistic fluid bodies