The control of the boundary layer for the micropolar fluid equations with zero limits of angular and microrotational viscosities

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In this paper, we consider an initial-boundary value problem to the two-dimensional incompressible micropolar fluid equations. Our main purpose is to study the boundary layer effects, and especially, we pay more attention to control the boundary layer as the angular and microrotational viscosities go to zero. It is shown that the boundary layer thickness can be controlled by the derivative of the boundary temperature with respect to time. As a matter of fact, the relationship between the boundary layer thickness (\(O(\gamma ^\beta )\)) and the time derivative of the boundary temperature can be found in (1.13). Meanwhile, we generalize the conclusion of Reference Chen et al. (Z Angew Math Phys 65:687–710, 2014).