Classical solutions for the compressible liquid crystal flows with nonnegative initial densities

AbstractIn this paper, we study the Cauchy problem of the simplified Ericksen–Leslie system modeling compressible nematic liquid crystal flows in R3. We first prove the local existence of the strong solutions provided that the data satisfies a natural compatibility condition. Then by deriving the smoothing effect of the solution in t>0, we conclude that it is indeed classical on some time interval [0,T0]. Here we do not need the condition that initial density is bounded below away from zero