On the well-posedness of relativistic viscous fluids with non-zero vorticity

TL;DR

This paper proves the well-posedness of a relativistic viscous fluid model with vorticity coupled to Einstein's equations, establishing existence, uniqueness, and finite propagation speed under certain conditions.

Contribution

It introduces a relativistic Navier-Stokes model with vorticity and proves its well-posedness and finite propagation speed when coupled with Einstein's equations.

Findings

Existence and uniqueness of solutions in Gevrey class

Finite propagation speed property established

Relativistic interpretation of vorticity condition

Abstract

We study the problem of coupling Einstein's equations to a relativistic and physically well-motivated version of the Navier-Stokes equations. Under a natural evolution condition for the vorticity, we prove existence and uniqueness in a suitable Gevrey class if the fluid is incompressible, where this condition is given an appropriate relativistic interpretation, and show that the solutions enjoy the finite propagation speed property.