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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.

35Q35PDEs in connection with fluid mechanics
76W05Magnetohydrodynamics and electrohydrodynamics
76M30Variational methods (fluid mechanics)
Full Text: DOI Link EuDML