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Magneto-micropolar fluid motion: Global existence of strong solutions. (English) Zbl 0976.35055
Summary: By using the spectral Galerkin method, we prove a result on global existence in time of strong solutions for the motion of a magneto-micropolar fluid ${\partial u\over\partial t}+u\cdot\nabla u- (\mu+\chi)\Delta u+ \nabla\Biggl(p+{1\over 2} rb\cdot b\Biggr)= \chi\text{ rot }w+ rb\cdot\nabla b+ f,$ $j{\partial w\over\partial t}+ ju\cdot\nabla w- \gamma\Delta w+ 2\chi w-(\alpha+ \beta)\nabla\text{ div } w= \chi\text{ rot }u+ g,$ ${\partial b\over\partial t}- \nu\Delta b+ u\cdot\nabla b- b\cdot\nabla u= 0,$ $\text{div }u= \text{div }b= 0\quad\text{in }(0,T)\times \Omega$ without assuming the external forces decay with time. We also derive uniform in time estimates of the solution that are usual for obtaining error bounds for the approximate solutions.

##### MSC:
 35Q35 PDEs in connection with fluid mechanics 76W05 Magnetohydrodynamics and electrohydrodynamics 76M30 Variational methods applied to problems in fluid mechanics
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