An optimal regularity criterion for the 3D MHD equations in homogeneous Besov spaces

Abstract

In this paper, we establish a new regularity criterion for weak solutions to the 3D incompressible MHD equations in terms of two pairs of (i u i , i b i) (i = 1, 2, 3). More precisely, it is proved that the weak solution (u, b) is smooth on (0, T], provided that for some i, j ∈ {1, 2, 3} with i ≠ j, it holds that