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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.02601 |
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Table of 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.