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arXiv · 2101.02410

On the global well-posedness of the 3D axisymmetric resistive MHD equations

Zineb Hassainia
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Abstract

In this paper, we prove the global well-posedness for the three-dimensional magnetohydrodynamics (MHD) equations with zero viscosity and axisymmetric initial data. First, we analyze the problem corresponding to the Sobolev regularities $ H^s\times H^{s-2}$, with $ s>5/2$. Second, we address the same problem but for the Besov critical regularities $ B_{p,1}^{3/p+1}\times B_{1,p}^{3/p-1}$, $2\leq p\leq \infty$. This case turns out to be more subtle as the Beale-Kato-Majda criterion is not known to be valid for rough regularities.

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Zineb Hassainia. 2021-01-07. On the global well-posedness of the 3D axisymmetric resistive MHD equations. https://doi.org/10.1007/s00023-021-01146-w

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