Global well-posedness for the micropolar fluid system in critical Besov spaces

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• 作者：Qionglei  ; Chen ;   ; ^{chen_qionglei@iapcm.ac.cn} ; Changxing  ; Miao ;   ; ^{miao_changxing@iapcm.ac.cn}
• 关键词：Micropolar fluid ; Global well-posedness ; Littlewood&ndash ; Paley decomposition ; Besov space ; Highly oscillating
• 刊名：Journal of Differential Equations
• 出版年：2012
• 出版时间：1 February 2012
• 年：2012
• 卷：252
• 期：3
• 页码：2698-2724
• 全文大小：294 K

文摘

We prove the global well-posedness for the 3-D micropolar fluid system in the critical Besov spaces by making a suitable transformation of the solutions and using the Fourier localization method, especially combined with a new estimate for the Green matrix to the linear system of the transformed equation. This result allows to construct global solutions for a class of highly oscillating initial data of Cannone?s type. Meanwhile, we analyze the long-time behavior of the solutions and get some decay estimates.