Methods and Applications of Analysis

Volume 25 (2018)

Number 2

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

Pages: 133 – 166

DOI: https://dx.doi.org/10.4310/MAA.2018.v25.n2.a4

Authors

Taynara B. De Souza (Departamento de Matemática, Universidade Federal de Sergipe, São Cristóvão, SE, Brazil)

Wilberclay G. Melo (Departamento de Matemática, Universidade Federal de Sergipe, São Cristóvão, SE, Brazil)

Paulo R. Zingano (Departamento de Matemática Pura e Aplicada, Universidade Federal do Rio Grande do Sul, Porto Alegre, RS Brazil)

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.

Keywords

magnethohydrodinamics equations, blow-up criteria, global existence of solution

2010 Mathematics Subject Classification

35Q40, 35Q60, 35Q61, 76W05

Received 11 December 2017

Accepted 6 November 2018

Published 3 January 2019