A regularity criterion of the 3D MHD equations involving one velocity and one current density component in Lorentz space

2020/05/07 by R. Agarwal, S. Gala, M. A. Ragusa · 1 citation
Mathematics · #math.AP #msc:35Q35 #msc:35B65 #msc:76D05

paper · pdf · doi:10.1007/s00033-020-01318-4

Zeitschrift für angewandte Mathematik und Physik

arxiv created 2020/05/07 · arxiv updated 2020/05/12

Abstract

In this paper, we study the regularity criterion of weak solutions to the three-dimensional (3D) MHD equations. It is proved that the solution (u,b) becomes regular provided that one velocity and one current density component of the solution satisfy% u₃∈ L^{(30α)/(7α-45)}( 0,T;L^α,∞ ( ℝ³) ) with (45)/(7)% ≤ α≤ ∞ , % and j₃∈ L^{(2β)/(2β-3)}( 0,T;L^β,∞ ( ℝ³) ) with (3)/(2)≤ β≤ ∞ , % which generalize some known results.

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