Global existence of large strong solutions to the 3D compressible micropolar equations with density-dependent viscosities

In this paper, we consider the Cauchy problem for the three-dimensional (3D) compressible micropolar equations with density-dependent viscosities. By classical $L^p$ estimates to elliptic system, defining suitable energy functions, after the elaborate index analysis, we establish the global existence of strong solutions to the system with all viscosities depending density as long as the initial density is large enough. By product, We also prove the existence of global large strong solutions with only large initial shear viscosity ${\mu }_1(\rho )$ and angular viscosity ${\mu }_2(\rho )$, which consists with the research work \cite{ZZ2014} of 3D compressible Navier-Stokes equations with constant viscosities and improve the recent result of \cite{HLZ} in some extent where they requiring both initial shear viscosity and bulk viscosity to be large.