On the local well-posedness for the relativistic Euler equations for a liquid body

TL;DR

This paper establishes local existence for the free boundary problem of a relativistic fluid in a fixed spacetime, using boundary derivative control, applicable also to Newtonian fluids.

Contribution

It introduces a novel a priori estimate that requires only tangential derivatives, advancing the mathematical understanding of relativistic fluid dynamics with free boundaries.

Findings

Proves local existence for relativistic fluid free boundary problems.

Develops an a priori estimate based on tangential derivatives.

Applicable to both relativistic and Newtonian fluid models.

Abstract

We prove a local existence theorem for the free boundary problem for a relativistic fluid in a fixed spacetime. Our proof involves an a priori estimate which only requires control of derivatives tangential to the boundary, which holds also in the Newtonian compressible case.