A priori estimates for relativistic liquid bodies

Understand

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.