Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5024697 | Nonlinear Analysis: Theory, Methods & Applications | 2017 | 16 Pages |
Abstract
This paper studies the global regularity of classical solutions to 2D magneto-micropolar fluid equations with only micro-rotational velocity dissipation and magnetic diffusion. Here the micro-rotational velocity dissipation and magnetic diffusion are given by âÎΩ and (âÎ)βb. Making use of several combined quantities, maximal regularity of heat operator and Littlewood-Paley decomposition theory, we establish a regularity criterion in terms of magnetic field for the case β=1 and the global regularity for β>1. The regularity criterion given here is also new even for the 2D magnetohydrodynamic equations. In addition, to prove these two main results, as preparation we establish a new global a priori estimate for magnetic field, namely ÎbâLâ(0,T;Lp(R2)) with pâ¥2 which also holds for the 2D magnetohydrodynamic equations as a particular case.
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Authors
Haifeng Shang, Jiefeng Zhao,