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arXiv · 1008.0219

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

Qionglei Chen·Changxing Miao
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Abstract

We prove the global well-posedness for the 3-D micropolar fluid system in the critical Besov spaces by making a suitable transformation to the solutions and using the Fourier localization method, especially combined with a new $L^p$ 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 behavior of the solutions and get some decay estimates.

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Qionglei Chen, Changxing Miao. 2010-08-02. Global well-posedness for the micropolar fluid system in the critical Besov spaces. https://doi.org/10.1016/j.jde.2011.09.035

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