Strongly hyperbolic quasilinear systems revisited, with applications to relativistic fluid dynamics

TL;DR

This paper revisits the theory of strongly hyperbolic quasilinear systems, providing a simple proof of well-posedness and applying it to relativistic fluid dynamics, with minimal regularity assumptions.

Contribution

It offers a self-contained proof of local well-posedness for strongly hyperbolic systems with minimal regularity, and applies these results to relativistic fluid models.

Findings

Established local well-posedness under minimal regularity.

Applied theory to ideal and viscous relativistic fluids.

Simplified the proof of well-posedness for strongly hyperbolic systems.

Abstract

We revisit the theory of first-order quasilinear systems with diagonalizable principal part and only real eigenvalues, what is commonly referred to as strongly hyperbolic systems. We provide a self-contained and simple proof of local well-posedness, in the Hadamard sense, of the Cauchy problem. Our regularity assumptions are very minimal. As an application, we apply our results to systems of ideal and viscous relativistic fluids, where the theory of strongly hyperbolic equations has been systematically used to study several systems of physical interest.