Recent developments on the micropolar and magneto-micropolar fluid systems: Deterministic and stochastic perspectives

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Abstract

We review recent developments on the micropolar and magnetomicropolar fluid systems in spatial dimensions two and three from both deterministic and stochastic perspectives. Under the deterministic setting, we review the global regularity result in two-dimensional space with zero angular viscosity and a regularity criterion in three-dimensional space that involves only two velocity vector field components. Under the stochastic setting, we review the existence of a weak martingale solution in three-dimensional space and the unique strong solution in twodimensional space under a suitable condition on the noise. Throughout the paper, we compare these results with other partial differential equations related to fluidmechanics, such as the Navier-Stokes equations, magnetohydrodynamics and Boussinesq systems.

Original languageEnglish
Pages (from-to)85-103
Number of pages19
JournalMathematical Engineering
Volume20
DOIs
StatePublished - 2015

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