Blow-Up Solution of the 3D Viscous Incompressible MHD System (Journal of Partial Differential Equations, 2020)
The 3D viscous incompressible magneto-hydrodynamic (MHD) system comprised by the 3D incompressible viscous Navier-Stokes equation couples with Maxwellequation. The global well-posedness of the coupled system is still an open problem. Inthis paper, we study the Cauchy problem of this coupled system and establish somelogarithmical type of blow-up criterion for smooth solution in Lorentz spaces.