Local existence and blow-up criterion for the two and three dimensional ideal magnetic Benard problem
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In this article, we consider the ideal magnetic Bénard 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.
CitationManna, U., & Panda, A. A. (2020). Local existence and blow-up criterion for the two and three dimensional ideal magnetic Benard problem. Electronic Journal of Differential Equations, 2020(91), pp. 1-26.
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