Manna, UtpalPanda, Akash Ashirbad2021-10-042021-10-042020-09-07Manna, 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. 1-26.1072-6691https://hdl.handle.net/10877/14598In 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.Text26 pages1 file (.pdf)enAttribution 4.0 InternationalMagnetic Benard problemCommutator estimatesBlow-up criterionLogarithmic Sobolev inequalityArticle