Classical solutions to a BGK-type model relaxing to the isentropic gas dynamics
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866909107319996416 |
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| author | Hwang, Byung-Hoon |
| author_facet | Hwang, Byung-Hoon |
| contents | In this paper, we consider a BGK-type kinetic model relaxing to the isentropic gas dynamics in the hydrodynamic limit. We introduce a linearization of the equation around the global equilibrium. Then we prove the global existence of classical solutions with an exponential convergence rate toward the equilibrium state in the periodic domain when the initial data is a small perturbation of the global equilibrium. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_09653 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Classical solutions to a BGK-type model relaxing to the isentropic gas dynamics Hwang, Byung-Hoon Analysis of PDEs In this paper, we consider a BGK-type kinetic model relaxing to the isentropic gas dynamics in the hydrodynamic limit. We introduce a linearization of the equation around the global equilibrium. Then we prove the global existence of classical solutions with an exponential convergence rate toward the equilibrium state in the periodic domain when the initial data is a small perturbation of the global equilibrium. |
| title | Classical solutions to a BGK-type model relaxing to the isentropic gas dynamics |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2402.09653 |