On regularity of the 3D MHD equations based on one velocity component in anisotropic Lebesgue spaces

In this paper we establish a new regularity criterion for the 3D incompressible MHD equations via partial derivative(3)u(3) and the magnetic field b. By considering different weights in spatial variables, we show in anisotropic Lebesgue spaces if partial derivative(3)u(3) and b satisfy certain space-time integrable conditions, which are almost optimal from the scaling invariant point of view, then a weak solution (u, b) is actually regular. This result gives new insights into the understanding of regularity theory of weak solutions. (C) 2021 Elsevier Ltd. All rights reserved.

Automated summary

This paper establishes a new regularity criterion for the 3D incompressible MHD equations by considering different weights in spatial variables. It shows that if certain space-time integrable conditions are satisfied by the partial derivatives and the magnetic field, then a weak solution is actually regular, providing new insights into the regularity theory of weak solutions.