Blow-Up Solution of the 3D Viscous Incompressible MHD System

Xin-Guang Yang; Wei Shi; Yongjin Lu

doi:10.4208/jpde.v33.n2.2

Authors

Xin-Guang Yang Department of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, China
Wei Shi Department of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, China
Yongjin Lu Department of Mathematics and Economics, Virginia State University, Petersburg, VA 23806, USA

DOI:

https://doi.org/10.4208/jpde.v33.n2.2

Keywords:

MHD equations, blow-up criteria, Lorentz space.

Abstract

The 3D viscous incompressible magneto-hydrodynamic (MHD) system comprised by the 3D incompressible viscous Navier-Stokes equation couples with Maxwell equation. The global well-posedness of the coupled system is still an open problem. In this paper, we study the Cauchy problem of this coupled system and establish some logarithmical type of blow-up criterion for smooth solution in Lorentz spaces.