Global solutions to 3D compressible MHD equations with partial magnetic diffusion
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866910931234062336 |
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| author | Wu, Jiahong Zhai, Xiaoping |
| author_facet | Wu, Jiahong Zhai, Xiaoping |
| contents | The global existence of strong solutions to the compressible viscous magnetohydrodynamic (MHD) equations in $\mathbb{R}^3$ remains a significant open problem. When there is no magnetic diffusion, even small data global well-posedness is unknown. This study investigates the Cauchy problem in $\mathbb{R}^3$ for the compressible viscous MHD equations with horizontal magnetic diffusion. Using various anisotropic Sobolev inequalities and sharp estimates, we establish the existence of global solutions under small initial data within the Sobolev space framework. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_04351 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Global solutions to 3D compressible MHD equations with partial magnetic diffusion Wu, Jiahong Zhai, Xiaoping Analysis of PDEs The global existence of strong solutions to the compressible viscous magnetohydrodynamic (MHD) equations in $\mathbb{R}^3$ remains a significant open problem. When there is no magnetic diffusion, even small data global well-posedness is unknown. This study investigates the Cauchy problem in $\mathbb{R}^3$ for the compressible viscous MHD equations with horizontal magnetic diffusion. Using various anisotropic Sobolev inequalities and sharp estimates, we establish the existence of global solutions under small initial data within the Sobolev space framework. |
| title | Global solutions to 3D compressible MHD equations with partial magnetic diffusion |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2505.04351 |