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arXiv:1706.05046 [math.AP]AbstractReferencesReviewsResources

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

Utpal Manna, Akash A. Panda

Published 2017-06-15Version 1

In this paper, we consider the ideal magnetic B\'{e}nard 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 $BMO$-norm of the vorticity and electrical current, generalising the Beale-Kato-Majda condition for ideal hydrodynamics.

Comments: 30 pages
Categories: math.AP
Subjects: 76D05, 76D03
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