Vanishing viscosity limit of the 2D micropolar equations for planar rarefaction wave to a Riemann problem

We are concerned with the vanishing viscosity limit of the 2D compressible micropolar equations to the Riemann solution of the 2D Euler equations which admit a planar rarefaction wave. In this article, the key point of the analysis is to introduce the hyperbolic wave, which helps us obtain the desired uniform estimates with respect to the viscosities. Moreover, the proper combining of rotation terms and damping term is also important, which contributes to closing the basic energy estimates. Finally, a family of smooth solutions for the 2D micropolar equations converging to the corresponding planar rarefaction wave solution with arbitrary strength is pursued.