LAUSR

Abstract The Cauchy problem for the three-dimensional non-isothermal model for compressible nematic liquid crystals is considered. Existence of global-in-time smooth solutions is established provided that the initial datum is close to a steady state ( ρ ¯ , 0 , d ¯ , θ ¯ ) . By using the L q – L p estimates and the Fourier splitting method, if the initial perturbation is small in H 3 -norm and bounded in L q ( q ∈ [ 1 , 6 5 ) ) norm, we obtain the optimal decay rates for the first and second order spatial derivatives of solutions. In addition, the third and fourth order spatial derivatives of director field d in L 2 -norm are achieved.