On the Equations of Compressible Fluid Dynamics With Cattaneo‐Type Extensions for the Heat Flux: Symmetrizability and Relaxation Structure
Year: 2024
Type: article
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.
Source: Studies in Applied Mathematics
DOI: 10.1111/sapm.12790
Author: Felipe Angeles
Institution: Universidad Nacional Autónoma de México
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4404763784