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

Abstract

We study compressible nematic liquid crystal flows with the bulk viscosity being a power function of the density (\(\lambda =\rho ^\beta \)) 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 \(\beta >\frac{4}{3}\). It should be noticed that there is no other restrictions on the size of initial data and the initial density allows vacuum states.