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

In this paper, we investigate the global existence and large-time behavior of strong solutions to two-dimensional compressible nematic liquid crystal flows in the periodic domain or in a bounded simply connected domain. The shear viscosity is assumed to be a positive constant, while the bulk viscosity is given by $\lambda (\rho )={\rho }^{\beta }$ with $\beta >4\mathrm{/}3$. For initial data allowing vacuum, we establish the global existence and uniqueness of strong solutions without any restrictions on the size of the initial data. In particular, no geometric angle condition is imposed on the initial orientation field. Moreover, we derive a time-uniform upper bound for the density and establish the exponential decay of the strong solutions toward equilibrium.