Forward self-similar solutions to the MHD equations: existence and pointwise estimates
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909537968062464 |
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| author | Yang, Yifan |
| author_facet | Yang, Yifan |
| contents | In this paper, we study the forward self-similar solutions to the three-dimensional Magnetohydrodynamic equations (MHD equations) in the whole space. By employing the Leray-Schauder theorem and blow-up argument, we construct a global-time forward self-similar solutions, which is smooth in $\R^{3}\times(0,\infty)$. Furthermore, by investigating the regularity of the weak solutions to the corresponding Leray system in the weighted Sobolev space, we can derive the pointwise estimate for the forward self-similar solution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_02601 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Forward self-similar solutions to the MHD equations: existence and pointwise estimates Yang, Yifan Analysis of PDEs In this paper, we study the forward self-similar solutions to the three-dimensional Magnetohydrodynamic equations (MHD equations) in the whole space. By employing the Leray-Schauder theorem and blow-up argument, we construct a global-time forward self-similar solutions, which is smooth in $\R^{3}\times(0,\infty)$. Furthermore, by investigating the regularity of the weak solutions to the corresponding Leray system in the weighted Sobolev space, we can derive the pointwise estimate for the forward self-similar solution. |
| title | Forward self-similar solutions to the MHD equations: existence and pointwise estimates |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2404.02601 |