Energy equality of the weak solutions to the fractional Navier-Stokes / MHD equations

Abstract: In this paper, we study the problem of energy equality for weak solutions of the 3D incompressible fractional Navier-Stokes / MHD equations. With the help of the technique of symmetrization and interpolation method, we obtain some new sufficient conditions including the Sobolev multiplier spaces, which insures the validity of the energy equality of the weak solution to fractional MHD equations. Correspondingly, the results of fractional Navier-Stokes equations are obtained. And these energy equations are usually related to the uniqueness of solutions to the corresponding fractional Navier-Stokes / MHD equations.