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1. Local existence and blow-up criterion for the two and three dimensional ideal magnetic Benard problem

Author

Utpal Manna and Akash Ashirbad Panda

Subjects
magnetic benard problem, commutator estimates, blow-up criterion, logarithmic sobolev inequality, Mathematics, QA1-939
Abstract

In this article, we consider the ideal magnetic Benard problem in both two and three dimensions and prove the existence and uniqueness of strong local-in-time solutions, in Hs for s > (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, generalizing the Beale-Kato-Majda condition for ideal hydrodynamics.

Published
2020

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