On some new global existence results for 3D magnetohydrodynamic equations

This paper is devoted to the incompressible magnetohydrodynamic 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 resulting in a global strong solution without the smallness restriction on the size of initial velocity or magnetic field. In other words, magnetic field can indeed regularize Navier-Stokes equations, due to cancellation.