On the Blow-up Criterion of Magnetohydrodynamics Equations in Homogeneous Sobolev Spaces

Abstract

In this paper, we obtain new lower bounds on the Homogeneous Sobolev--norms of the maximal solution of the Magnetohydrodynamics Equations. This gives us some insight on the blow-up behavior of the solution. We utilize standard techniques from the Navier--Stokes Equations.

9 pages