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Regularity criteria of weak solutions to the three-dimensional micropolar flows. (English) Zbl 1283.76016
Summary: Regularity criteria of weak solutions to the three-dimensional micropolar fluid motion equations are discussed. Sufficient conditions for the regularity of weak solutions are presented by imposing Serrin’s type growth conditions on the velocity field in Lorentz spaces, multiplier spaces, bounded mean oscillation spaces, and Besov spaces, respectively. The findings demonstrate that the velocity field plays a dominant role in the regularity problem of micropolar fluid motion equations.
©2009 American Institute of Physics

MSC:
76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
35B65 Smoothness and regularity of solutions to PDEs
35Q35 PDEs in connection with fluid mechanics
76A05 Non-Newtonian fluids
76U05 General theory of rotating fluids
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