(untitled) (Communications in Mathematical Research, 2022)
The regularity for 3-D MHD equations is considered in this paper. It is proved that the solutions (v,B,p) are Hölder continuous if the velocity field vL^∞(0,T;L^3,∞_x (R^3)) with local small condition r^−3|{ x∈B_r(x_0):|v(x,t_0)|>εr^−1}|≤ε and the magnetic field B∈L^ ∞(0,T;VMO^−1 (R^3)).