On some new global existence result of 3D Magnetohydrodynamic equations

Abstract

This paper is devoted to the incompressible Magenetohydrodynamic equations in $\R^3$. We prove that if the difference between the magnetic field and the velocity is small initially then it will remain forever, thus results in global strong solution without smallness restriction on the size of initial velocity or magnetic field. In other words, magnetic field can indeed regularize the Navier-Stokes equations, due to cancelation.