An improved regularity criterion of three-dimensional magnetohydrodynamic equations

An improved regularity criterion for a weak solution of three-dimensional magnetohydrodynamic equations is obtained. Employing the Fourier localization technique, it is proved that weak solutions become regular on (0,T](0,T] if the summation of velocity field uu and magnetic field bb belong to the largest critical spaces: u+b∈L21+r(0,T;B∞,∞r(R3)),−1