Relativistic dissipative fluids in the trace-fixed particle frame: Strongly hyperbolic quasi-linear first-order evolution equations

TL;DR

This paper develops a new first-order relativistic dissipative fluid theory in the trace-fixed particle frame, demonstrating that the resulting equations are strongly hyperbolic, causal, stable, and well-posed for initial value problems.

Contribution

It introduces a novel first-order formulation of relativistic dissipative fluids that ensures strong hyperbolicity and well-posedness, advancing the mathematical foundation of such theories.

Findings

The system is strongly hyperbolic and causal.

Auxiliary constraints propagate, ensuring consistency.

The theory is stable at global equilibrium states.

Abstract

In this paper we derive a new first-order theory of relativistic dissipative fluids by adopting the trace-fixed particle frame. Whereas in a companion letter we show that this theory is hyperbolic, causal and stable at global equilibrium states, here we prove that the full nonlinear system of equations can be cast into a first-order quasilinear system which is strongly hyperbolic. By rewriting the system in first-order form, auxiliary constraints are introduced. However, we show that these constraints propagate, and thus our theory leads to a well-posed Cauchy problem.