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

By Qionglei Chen, Changxing Miao. 2010

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

Subfields: Applied Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d84796ec316a890290cd960c234414a9a9c787b9