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Zbl 1137.76071
Yuan, Jia
Existence theorem and blow-up criterion of the strong solutions to the magneto-micropolar fluid equations. (English)
[J] Math. Methods Appl. Sci. 31, No. 9, 1113-1130 (2008). ISSN 0170-4214; ISSN 1099-1476/e

Summary: We study the magneto-micropolar fluid equations in $\mathbb R^{3}$, prove the existence of strong solution with initial data in $H^s(\mathbb R^3)$ for $s> \frac 3 2$, and set up its blow-up criterion. The tool we mainly use is Littlewood-Paley decomposition, by which we obtain a Beale-Kato-Majda-type blow-up criterion for smooth solution $(u,\omega , b)$ that relies on the vorticity of velocity $\nabla \times u$ only.

MSC 2000:: *76W05 Flows in presence of electromagnetic forces
35Q35 Other equations arising in fluid mechanics
35Q60 PDE of electromagnetic theory and optics

Keywords: Littlewood-Paley decomposition; Besov space; Beale-Kato-Majda criterion

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Zentralblatt MATH Berlin [Germany]