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

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

2010-08-02

arxiv.org/abs/1008.0219v1

J. Differential Equations, 252 (2012) 2698-2724

Mathematics

Analysis of PDEs

23pages

Scientific paper

10.1016/j.jde.2011.09.035

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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