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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.00844 |
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| _version_ | 1866916270860926976 |
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| author | Angeles, Felipe |
| author_facet | Angeles, Felipe |
| contents | 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, i.e., solutions preserving the $L^{2}$ norm for all times that are not dissipated by the relaxation terms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_00844 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the equations of compressible fluid dynamics with Cattaneo-type extensions for the heat flux: Symmetrizability and relaxation structure Angeles, Felipe Analysis of PDEs 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, i.e., solutions preserving the $L^{2}$ norm for all times that are not dissipated by the relaxation terms. |
| title | On the equations of compressible fluid dynamics with Cattaneo-type extensions for the heat flux: Symmetrizability and relaxation structure |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2406.00844 |