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

2022/03/02 by Alghamdi, Ahmad M., Gala, Sadek, Ragusa, Maria Alessandra
#35B65 #76D05 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2203.01115

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 \fracπ( e^-\vert x\vert ²+\vert u\vert +\vert b\vert ) ^θ∈ L^p(0,T;L^q,∞ (ℝ³)), where (2)/(p)+(3)/(% q)=2-θ and 0≤ θ≤ 1.

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