Global Well-Posedness of Strong Solutions to the Two-Dimensional Compressible Nematic Liquid Crystal Flows with Large Initial Data and Vacuum

This paper concerns the global well-posedness of two-dimensional compressible nematic liquid crystal flows in the whole space or in the half-space. Under the assumptions that the shear viscosity is a positive constant and that the bulk viscosity is given by $λ(ρ)=ρ^β$ with $β>4/3$, we establish the