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

2017/06/15 by Utpal Manna, Manna, Utpal, Akash Ashirbad Panda +2
Mathematics · #76D03 #76D05 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations #math.AP #msc:76D03 #msc:76D05

paper · pdf · doi:10.48550/arxiv.1706.05046

30 pages

arxiv created 2017/06/15 · openalex publication_date 2017/06/15 · arxiv updated 2017/06/19 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider the ideal magnetic Bénard problem in both two and three dimensions and prove local-in-time existence and uniqueness of strong solutions in H^s 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, generalising the Beale-Kato-Majda condition for ideal hydrodynamics.

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