On The Two and Three Dimensional Ideal Magnetic B\'enard Problem - Local Existence and Blow-up Criterion
Abstract
In this paper, we consider the ideal magnetic B\'enard problem in both two and three dimensions and prove local-in-time existence and uniqueness of strong solutions in Hs for s > n2+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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