Strong solutions to the Cauchy problem of two-dimensional compressible non-isothermal nematic liquid crystal flows with vacuum and zero heat conduction

Abstract

We study the Cauchy problem of nonisothermal compressible nematic liquid crystal flows involving zero heat conduction on the whole two-dimensional (2D) space with vacuum at infinity. For the initial density allowing vacuum states, we prove that there exists a local strong solution, provided that the initial data density and the gradient of orientation decay not too slowly at infinity. Our method relies on delicate weighted energy estimates and a Hardy-type inequality.