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

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.

23pages

References in corpus (2)

• Global well-posedness for the compressible Navier-Stokes equations with the highly oscillating initial velocity
• Existence theorem and blow-up criterion of the strong solutions to the Magneto-micropolar fluid equations

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• A class large solution of 3D incompressible micropolar fluid system
• Convergence rate of solutions toward stationary solutions to the isentropic micropolar fluid model in a half line
• Asymptotic behavior of global weak solutions for the micropolar dynamics in $L^2({\mathbb{R}}^3)$
• Sharp well-posedness and ill-posedness for the 3-D micropolar fluid system in Fourier-Besov spaces
• Well-posedness of compressible magneto-micropolar fluid equations