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Zbl 1078.35096
Yamaguchi, Norikazu
Existence of global strong solution to the micropolar fluid system in a bounded domain. (English)
[J] Math. Methods Appl. Sci. 28, No. 13, 1507-1526 (2005). ISSN 0170-4214; ISSN 1099-1476/e

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 2000:: *35Q35 Other equations arising in fluid mechanics
76D03 Existence, uniqueness, and regularity theory
76A05 Non-Newtonian fluids
76W05 Flows in presence of electromagnetic forces

Keywords: micropolar fluid; magneto-micropolar fluid; resolvent estimates; global existence; analytic semigroup

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