A priori estimates for relativistic liquid bodies

作者：Oliynyk, Todd A.^*

来源：Bulletin des Sciences Mathematiques, 2017, 141(3): 105-222.

DOI：10.1016/j.bulsci.2017.02.001

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

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.

• 出版日期2017-5