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

Article type: Research Article

Authors: Disconzi, Marcelo M.^{a; *} | Shao, Yuanzhen^b

Affiliations: [a] Vanderbilt University, Nashville, TN, USA | [b] The University of Alabama, Tuscaloosa, AL, USA

Correspondence: [*] Corresponding author. E-mail: marcelo.disconzi@vanderbilt.edu.

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.

Keywords: Strong hyperbolicity, first-order quasilinear systems, relativistic fluids

DOI: 10.3233/ASY-241919

Journal: Asymptotic Analysis, vol. 140, no. 3-4, pp. 281-302, 2024