On The Two and Three Dimensional Ideal Magnetic Bénard Problem - Local Existence and Blow-up Criterion

In this paper, we consider the ideal magnetic B\'{e}nard problem in both two and three dimensions and prove local-in-time existence and uniqueness of strong solutions in \(H^s\) for \(s > \frac{n}{2}+1, n = 2,3\). In addition, a necessary condition is derived for singularity development with...

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Bibliographic Details
Published in:arXiv.org 2017-06
Main Authors: Manna, Utpal, Panda, Akash A
Format: Article
Language:English
Subjects:
Fluid dynamics
Fluid flow
Hydrodynamics
Vorticity
Online Access:Get full text
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Summary:In this paper, we consider the ideal magnetic B\'{e}nard problem in both two and three dimensions and prove local-in-time existence and uniqueness of strong solutions in \(H^s\) for \(s > \frac{n}{2}+1, n = 2,3\). In addition, a necessary condition is derived for singularity development with respect to the \(BMO\)-norm of the vorticity and electrical current, generalising the Beale-Kato-Majda condition for ideal hydrodynamics.
ISSN:2331-8422