3D Hall-MHD system with vorticity in Besov spaces
Volume 121 / 2018
Annales Polonici Mathematici 121 (2018), 91-98
MSC: Primary 35Q35; Secondary 35B65, 35Q85, 76W05.
DOI: 10.4064/ap170717-8-4
Published online: 21 May 2018
Abstract
By introducing some new ideas, using the methods from Z. Ye [Nonlinear Anal. 144 (2016), 182–193] and Z. Ye and Z. J. Zhang [Appl. Math. Comput. 301 (2017), 70–77] and the result of Z. J. Zhang [J. Math. Anal. Appl. 441 (2016), 692–701], we establish the regularity criterion $$ \boldsymbol{\omega} \in L^{2/s}(0,T;\dot B^s_{\infty ,\infty }(\mathbb {R}^3)),\ \hskip 1em 0 \lt s \lt 1, $$ for the $3$D Hall-MHD system. This improves several previous results.
