Regularity for 3-D MHD Equations in Lorentz Space $L^{3,∞}$

Abstract

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 v∈L∞(0,T;L x (R 3)) with local small condition r ∣∣ { x∈Br(x0) : |v(x,t0)|> εr −1 ∣∣≤ ε and the magnetic field B∈L∞(0,T;VMO−1(R3)). AMS subject classifications: 35Q35, 76B03, 76D03