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3D Hall-MHD system with vorticity in Besov spaces. (English) Zbl 1421.35297
Summary: By introducing some new ideas, using the methods from Z. Ye [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 144, 182–193 (2016; Zbl 1348.35206)] and Z. Ye and Z. Zhang [Appl. Math. Comput. 301, 70–77 (2017; Zbl 1411.35232)] and the result of Z. Zhang [J. Math. Anal. Appl. 441, No. 2, 692–701 (2016; Zbl 1338.35077)], we establish the regularity criterion $\boldsymbol{\omega} \in L^{2/s}(0,T;\dot B^s_{\infty ,\infty}(\mathbb R^3)),\;\hskip 1em 0 < s < 1,$ for the $$3$$D Hall-MHD system. This improves several previous results.
##### MSC:
 35Q35 PDEs in connection with fluid mechanics 35B65 Smoothness and regularity of solutions to PDEs 35Q85 PDEs in connection with astronomy and astrophysics 76W05 Magnetohydrodynamics and electrohydrodynamics 85A30 Hydrodynamic and hydromagnetic problems in astronomy and astrophysics
##### Keywords:
Hall-MHD system; regularity criteria; vorticity
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##### References:
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