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arXiv · 1706.05046

On The Two and Three Dimensional Ideal Magnetic B\'enard Problem - Local Existence and Blow-up Criterion

Utpal Manna·Akash A. Panda
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Abstract

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.

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Utpal Manna, Akash A. Panda. 2017-06-15. On The Two and Three Dimensional Ideal Magnetic B\'enard Problem - Local Existence and Blow-up Criterion. https://arxiv.org/abs/1706.05046

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