Non-uniform Continuity for the MHD equations with only Magnetic Diffusion
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910013957603328 |
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| author | Jiu, Quansen Xie, Yaowei |
| author_facet | Jiu, Quansen Xie, Yaowei |
| contents | In this paper, we prove the non-uniform continuity of the data-to-solution map for the incompressible magnetohydrodynamic (MHD) equations with only magnetic diffusion in Sobolev spaces $H^s(\mathbb{R}^d)$ for all $s>0$ and $d=2,3$. Our results are first studies on the non-uniform continuity of the data-to-solution map for the resistive MHD equations. Moreover, our results permit the solution perturbation around an arbitrary constant background magnetic fields $\mathbf{B_0} \in \mathbb{R}^d$, which reveal that the strong magnetic background fields may provide the stabilization effect but still preserve the analytical feature of non-uniform continuity of the data-to-solution map. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_06332 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Non-uniform Continuity for the MHD equations with only Magnetic Diffusion Jiu, Quansen Xie, Yaowei Analysis of PDEs In this paper, we prove the non-uniform continuity of the data-to-solution map for the incompressible magnetohydrodynamic (MHD) equations with only magnetic diffusion in Sobolev spaces $H^s(\mathbb{R}^d)$ for all $s>0$ and $d=2,3$. Our results are first studies on the non-uniform continuity of the data-to-solution map for the resistive MHD equations. Moreover, our results permit the solution perturbation around an arbitrary constant background magnetic fields $\mathbf{B_0} \in \mathbb{R}^d$, which reveal that the strong magnetic background fields may provide the stabilization effect but still preserve the analytical feature of non-uniform continuity of the data-to-solution map. |
| title | Non-uniform Continuity for the MHD equations with only Magnetic Diffusion |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2602.06332 |