Global solution to the nematic liquid crystal flows with heat effect

The temperature-dependent incompressible nematic liquid crystal flows in a bounded domain Omega subset of R-N (N = 2, 3) are studied in this paper. Following Danchin's method in [7], we use a localization argument to recover the maximal regularity of Stokes equation with variable viscosity, by which we first prove the local existence of a unique strong solution, then extend it to a global one provided that the initial data is a sufficiently small perturbation around the trivial equilibrium state. This paper also generalizes Hu-Wang's result in [21] to the non-isothermal case. (C) 2017 Elsevier Inc. All rights reserved.