Global well-posedness to the Cauchy problem of 2D compressible nematic liquid crystal flows with large initial data and vacuum

We study compressible nematic liquid crystal flows with the bulk viscosity being a power function of the density ( \(\lambda =\rho ^\beta \) $\lambda ={\rho }^{\beta }$ ) on the whole two-dimensional (2D) plane. Under a geometric angle condition for the initial direction field, we show the global existence and uniqueness of strong solutions provided that \(\beta >\frac{4}{3}\) $\beta >\frac{4}{3}$ . It should be noticed that there is no other restrictions on the size of initial data and the initial density allows vacuum states.