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arXiv · 2203.01115

A regularity criterion of 3D incompressible MHD system with mixed pressure-velocity-magnetic field

Ahmad M. Alghamdi·Sadek Gala·Maria Alessandra Ragusa
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Abstract

This work focuses on the 3D incompressible magnetohydrodynamic (MHD) equations with mixed pressure-velocity-magnetic field in view of Lorentz spaces. Our main result shows the weak solution is regular, provided that $${\frac{\pi }{\left( e^{-\left\vert x\right\vert ^{2}}+\left\vert u\right\vert +\left\vert b\right\vert \right) ^{\theta }}\in L}^{p}(0,T;L^{q,\infty }(\mathbb{R}^{3})),\text{ where }\frac{2}{p}+\frac{3}{% q}=2-\theta \text{ and }0\leq \theta \leq 1.$$

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Ahmad M. Alghamdi, Sadek Gala, Maria Alessandra Ragusa. 2022-03-02. A regularity criterion of 3D incompressible MHD system with mixed pressure-velocity-magnetic field. https://arxiv.org/abs/2203.01115

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