Optimal Decay Estimates for the 2D Micropolar Equations with Mixed Velocity Dissipation

This paper investigates the large time behavior of solutions to the 2D micropolar equations with partial dissipation. When there is mixed velocity dissipation and positive angular viscosity, we obtain the optimal decay estimates to the global solutions and their higher order derivatives without any small assumptions on the initial data. Moreover, when there is mixed velocity dissipation only, we prove the existence and upper bounds of decay estimates of the global strong solutions provided that the initial data is sufficiently small.