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 $\lambda (\rho )={\rho }^{\beta }$ with $\beta >4\mathrm{/}3$, we establish the global existence and uniqueness of strong solutions. It should be mentioned that our results are obtained without any restrictions on the size of the initial data and allow for the presence of vacuum. In particular, the initial orientation field is not required to satisfy any geometric angle condition.