On The Two and Three Dimensional Ideal Magnetic B\'enard Problem - Local Existence and Blow-up Criterion

Utpal Manna; Akash A. Panda

On The Two and Three Dimensional Ideal Magnetic B\'enard Problem - Local Existence and Blow-up Criterion

Analysis of PDEs 2017-06-19 v1

Authors: Utpal Manna , Akash A. Panda

Abstract

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.

Keywords

ideal magnetic Bénard problem local existence blow-up criterion Beale-Kato-Majda condition strong solutions

Cite

@article{arxiv.1706.05046,
  title  = {On The Two and Three Dimensional Ideal Magnetic B\'enard Problem - Local Existence and Blow-up Criterion},
  author = {Utpal Manna and Akash A. Panda},
  journal= {arXiv preprint arXiv:1706.05046},
  year   = {2017}
}

Comments

30 pages

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