On lower bounds for the solution, and its spatial derivatives, of the Magnetohydrodynamics Equations in Lebesgue spaces

Abstract

. In this paper, the authors establish lower bounds for the usual Lebesgue norms of the maximal solution of the Magnetohydrodynamics Equations and present some criteria for global existence of solution. Thus, we can understand better on the blow-up behavior of this same solution. In addition, it is important to point out that we reach our main results by using standard techniques obtained from Navier-Stokes Equations.