A priori estimates for solutions to the relativistic Euler equations with a moving vacuum boundary

Understand

We study the relativistic Euler equations on the Minkowski spacetime background.

• We make assumptions on the equation of state and the initial data that are relativistic analogs of the well-known physical vacuum boundary condition, which has played an important role in prior work on the non-relativistic compressible Euler equations.
• Our main result is the derivation, relative to Lagrangian (also known as co-moving) coordinates, of local-in-time a priori estimates for the solution.
• The solution features a fluid-vacuum boundary, transported by the fluid four-velocity, along which the hyperbolicity of the equations degenerates.