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

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 Lp 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 Cannoneʼs type. Meanwhile, we analyze the long-time behavior of the solutions and get some decay estimates.