TY - JOUR
T1 - Recent developments on the micropolar and magneto-micropolar fluid systems
T2 - Deterministic and stochastic perspectives
AU - Yamazaki, Kazuo
N1 - Publisher Copyright:
© Springer International Publishing Switzerland 2015
PY - 2015
Y1 - 2015
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84929074057&partnerID=8YFLogxK
U2 - 10.1007/978-3-319-18206-3_4
DO - 10.1007/978-3-319-18206-3_4
M3 - Article
AN - SCOPUS:84929074057
SN - 2192-4732
VL - 20
SP - 85
EP - 103
JO - Mathematical Engineering
JF - Mathematical Engineering
ER -