Regularity for 3D MHD equations in Lorentz space

We shall consider the regularity for 3D MHD equations in this paper. When the velocity field is bounded in a critical space and the magnetic field satisfies a weaker condition, it can be concluded that the weak solution of MHD equation is a smooth solution. We prove that the weak solutions are Holder continuous if the velocity field belongs to some Lorentz space and the magnetic field belongs to a bigger space than Lorentz space, that is the magnetic field satisfies an even weaker condition than the velocity filed. Our main mathematical tool is the backward uniqueness theory for the parabolic operators established by Escauriaza, Seregin and. Sverak.