Global well-posedness to the 3D Cauchy problem of compressible non-isothermal nematic liquid crystal flows with vacuum

We are concerned with global well-posedness of strong solutions to the Cauchy problem for compressible non-isothermal nematic liquid crystal flows with vacuum as far field density in R-3. By using energy method, we establish the global existence and uniqueness of strong solutions provided that the quantity parallel to rho(0)parallel to L infinity + parallel to del d(0)parallel to L-3 is suitably small and the viscosity coefficients verify 3 mu > lambda. In particular, the initial density can even have compact support. When d is a constant vector and vertical bar d vertical bar = 1, we also extend partially the corresponding result in Li (2020) where the global small solution of full compressible Navier-Stokes equations was obtained under the condition 2 mu > lambda. To our knowledge, the result in this paper could be viewed as the first one on the global existence of strong solutions to 3D Cauchy problem for compressible non-isothermal nematic liquid crystal flows with vacuum. (C) 2020 Elsevier Ltd. All rights reserved.