Remarks on Ruggeri's First Model of Dissipative Fluid Dynamics as a Symmetric Hyperbolic System

TL;DR

This paper analyzes Ruggeri's first model of dissipative fluid dynamics, demonstrating its properties as a symmetric hyperbolic system and its convergence to Navier-Stokes-Fourier solutions, with stability results for barotropic fluids.

Contribution

It establishes the symmetric hyperbolic nature of Ruggeri's model and extends convergence and stability results to barotropic fluids.

Findings

Solutions converge to Navier-Stokes-Fourier equations

Homogeneous solutions are nonlinearly asymptotically stable

Model properties support Rational Extended Thermodynamics

Abstract

This note establishes properties of a model of dissipative fluid dynamics as a symmetric hyperbolic system by which Ruggeri once triggered the development of Rational Extended Thermodynamics. These properties, i.e., (1) convergence of solutions to those of the Navier-Stokes-Fourier equations and (2) nonlinear asymptotic stability of homogeneous reference solutions, also hold in the analogous situation for barotropic fluids.