The Boundary Effects and Zero Angular and Micro-rotational Viscosities Limits of the Micropolar Fluid Equations

摘要

In this paper, we consider an initial-value problem to the two-dimensional incompressible micropolar fluid equations. Our main purpose is to study the boundary layer effects as the angular and micro-rotational viscosities go to zero. It is also shown that the boundary layer thickness is of the order O (gamma(beta)) with (0 < beta < 2/3). In contrast with Chen et al. (Z. Angew. Math. Phys. 65:687-710, 2014), the BL-thickness we got is thinner than that in Chen et al. (Z. Angew. Math. Phys. 65:687-710, 2014). In addition, the convergence rates are also improved.