Global regularity for 2D magneto-micropolar equations with only micro-rotational velocity dissipation and magnetic diffusion

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• 作者：Haifeng Shang ; ^{hfshang@163.com} ; ^{hfshang@hpu.edu.cn} ; Jiefeng Zhao ^{zhaojiefeng001@163.com}
• 关键词：35Q35 ; 35B65 ; 76W05
• 刊名：Nonlinear Analysis: Theory, Methods & Applications
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：150
• 期：Complete
• 页码：194-209
• 全文大小：697 K
• 卷排序：150

文摘

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 −ΔΩ−ΔΩ and (−Δ)βb(−Δ)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=1β=1 and the global regularity for β>1β>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 Δb∈L∞(0,T;Lp(R2))Δb∈L∞(0,T;Lp(R2)) with p≥2p≥2 which also holds for the 2D magnetohydrodynamic equations as a particular case.