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Existence of global strong solution to the micropolar fluid system in a bounded domain. (English) Zbl 1078.35096
Summary: We are concerned with the initial boundary value problem of the micropolar fluid system in a three dimensional bounded domain. We study the resolvent problem of the linearized equations and prove the generation of analytic semigroup and its time decay estimates. In particular, ${L}^{p}$-${L}^{q}$ type estimates are obtained. By use of the ${L}^{p}$-${L}^{q}$ estimates for the semigroup, we prove the existence theorem of global in time solution to the original nonlinear problem for small initial data. Furthermore, we study the magneto-micropolar fluid system in the final section.
##### MSC:
 35Q35 PDEs in connection with fluid mechanics 76D03 Existence, uniqueness, and regularity theory 76A05 Non-Newtonian fluids 76W05 Magnetohydrodynamics and electrohydrodynamics