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arXiv · 2310.17398

Global existence of solutions for the Hall-MHD equations

TongKeun Chang·Bataa Lkhagvasuren·MinSuk Yang
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Abstract

In this paper, we study the global well-posedness of the incompressible Hall-MHD system for small initial data $( u_0, b_0) \in \dot B^{\frac3p -1}_{p,5} (\mathbb{R}) \times \Big( \dot B^{\frac3p -1}_{p,5} (\mathbb{R}) \cap \dot B^{\frac3p}_{p,1}(\mathbb{R}) \Big)$ for $1 < p < 5$. We get the result under the weaker regularity and integrability conditions of the initial data than the previous works. We also give integral formulae for the solution.

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TongKeun Chang, Bataa Lkhagvasuren, MinSuk Yang. 2023-10-26. Global existence of solutions for the Hall-MHD equations. https://arxiv.org/abs/2310.17398

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