Methods and Applications of Analysis
Volume 25 (2018)
On lower bounds for the solution, and its spatial derivatives, of the Magnetohydrodynamics Equations in Lebesgue spaces
Pages: 133 – 166
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.
magnethohydrodinamics equations, blow-up criteria, global existence of solution
2010 Mathematics Subject Classification
35Q40, 35Q60, 35Q61, 76W05
The first author was partially supported by Fapitec grant 8670.334.21669.10012014.
Received 11 December 2017
Accepted 6 November 2018
Published 3 January 2019