A Blow-Up Criterion for 3D Nonhomogeneous Incompressible Magnetohydrodynamic Equations with Vacuum

Abstract

For the strong solutions of the nonhomogeneous incompressible magnetohydrodynamics (MHD) system with vacuum, we establish a blow-up criterion for this system in terms of uC0,T;L3ℝ3. Moreover, the result generalizes previous ones in Giga (1986) and He and Xin (2005) where homogeneous incompressible Navier-Stokes equations and homogeneous incompressible MHD system are considered, respectively, and demonstrates that the velocity field plays a more dominant role in the MHD system.