A general Liouville-type theorem for the 3D steady-state Magnetic-Bénard system
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913398363521024 |
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| author | Jarrin, Oscar |
| author_facet | Jarrin, Oscar |
| contents | We establish a Liouville-type theorem for the elliptic and incompressible Magnetic-Bénard system defined over the entire three-dimensional space. Specifically, we demonstrate the uniqueness of trivial solutions under the condition that they belong to certain local Morrey spaces. Our results generalize in two key directions: firstly, the Magnetic-Bénard system encompasses other significant coupled systems for which the Liouville problem has not been previously studied, including the Boussinesq system, the MHD-Boussinesq system, and the Bénard system. Secondly, by employing local Morrey spaces, our theorem applies to Lebesgue spaces, Lorentz spaces, Morrey spaces, and certain weighted-Lebesgue spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_13952 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A general Liouville-type theorem for the 3D steady-state Magnetic-Bénard system Jarrin, Oscar Analysis of PDEs We establish a Liouville-type theorem for the elliptic and incompressible Magnetic-Bénard system defined over the entire three-dimensional space. Specifically, we demonstrate the uniqueness of trivial solutions under the condition that they belong to certain local Morrey spaces. Our results generalize in two key directions: firstly, the Magnetic-Bénard system encompasses other significant coupled systems for which the Liouville problem has not been previously studied, including the Boussinesq system, the MHD-Boussinesq system, and the Bénard system. Secondly, by employing local Morrey spaces, our theorem applies to Lebesgue spaces, Lorentz spaces, Morrey spaces, and certain weighted-Lebesgue spaces. |
| title | A general Liouville-type theorem for the 3D steady-state Magnetic-Bénard system |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2406.13952 |