Vanishing Micro-Rotation and Angular Viscosities Limit for the 2D Micropolar Equations in a Bounded Domain

Abstract

In this paper, we investigate the vanishing micro-rotation and angular viscosities limit of solutions to the 2D incompressible micropolar equations in a bounded domain with Navier-type boundary conditions satisfied by the velocity field. In a general bounded smooth domain \(\Omega \), we establish the uniform \(H^{2}(\Omega )\) estimates (independent of the micro-rotation and angular viscosities) of global strong solutions and prove the rate of convergence of viscosity solutions to the inviscid solutions in \(C(0,T;H^{1}(\Omega ))\) for any \(T>0\).