Uniqueness and time decay rate of weak solution to the 3D Voigt-regularized magnetohydrodynamic equations

Abstract

In this paper, the influence of the Voigt term −α∆ut on the wellposedness of the Magnetohydrodynamical (MHD) equations is considered. Especially, the L p estimate of the magnetic field is established by using the regularity of fluid velocity. Then, the uniqueness for weak solution of the 3D Voigt-regularized Magnetohydrodynamical model is obtained. Finally, the time decay rate for the weak solution of this MHD-Voigt equations is established by the Fourier splitting method.