On the Equations of Compressible Fluid Dynamics With Cattaneo‐Type Extensions for the Heat Flux: Symmetrizability and Relaxation Structure

2024/11/27 by Felipe Angeles, Felipe Ángeles
Mathematics · Engineering · #Navier-Stokes equation solutions #Thermoelastic and Magnetoelastic Phenomena #Gas Dynamics and Kinetic Theory

paper · doi:10.1111/sapm.12790

Abstract

ABSTRACT The aim of this work is twofold. From a mathematical point of view, we show the existence of a hyperbolic system of equations that is not symmetrizable in the sense of Friedrichs. Such system appears in the theory of compressible fluid dynamics with Cattaneo‐type extensions for the heat flux. In contrast, the linearizations of such system around constant equilibrium solutions have Friedrichs symmetrizers. Then, from a physical perspective, we aim to understand the relaxation term appearing in this system. By noticing the violation of the Kawashima–Shizuta condition, locally and smoothly, with respect to the Fourier frequencies, we construct persistent waves, that is, solutions preserving the norm for all times that are not dissipated by the relaxation terms.

Citations

• The Cauchy problem for quasi-linear symmetric hyperbolic systems
• Shock waves in arbitrary fluids
• On Relaxation Hyperbolic Systems Violating the Shizuta–Kawashima Condition

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