Local existence and blow-up criterion for the two and three dimensional ideal magnetic Benard problem
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Date
2020-09-07
Authors
Manna, Utpal
Panda, Akash Ashirbad
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
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.
Description
Keywords
Magnetic Benard problem, Commutator estimates, Blow-up criterion, Logarithmic Sobolev inequality
Citation
Manna, U., & Panda, A. A. (2020). Local existence and blow-up criterion for the two and three dimensional ideal magnetic Benard problem. <i>Electronic Journal of Differential Equations, 2020</i>(91), pp. 1-26.
Rights
Attribution 4.0 International