On The Two and Three Dimensional Ideal Magnetic Bénard Problem - Local Existence and Blow-up Criterion

Utpal Manna; Akash A. Panda

paper

On The Two and Three Dimensional Ideal Magnetic Bénard Problem - Local Existence and Blow-up Criterion

arXiv:1706.05046

Abstract

In this paper, we consider the ideal magnetic Bénard problem in both two and three dimensions and prove local-in-time existence and uniqueness of strong solutions in $H^{s}$ for $s > \frac{n}{2} + 1, n = 2, 3$ . In addition, a necessary condition is derived for singularity development with respect to the $B M O$ -norm of the vorticity and electrical current, generalising the Beale-Kato-Majda condition for ideal hydrodynamics.

30 pages