Lower bounds of solutions of the Magnetohydrodynamics Equations in Homogeneous Sobolev Spaces

Diego Marcon; Wilberclay Melo; Lineia Schütz; Juliana Sartori Ziebell

doi:10.5540/03.2017.005.01.0031

Lower bounds of solutions of the Magnetohydrodynamics Equations in Homogeneous Sobolev Spaces

Authors

Diego Marcon
Wilberclay Melo
Lineia Schütz
Juliana Sartori Ziebell

DOI:

https://doi.org/10.5540/03.2017.005.01.0031

Keywords:

Magnethohydrodinamics equations, blow-up criterion, lower bounds.

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.