Abstract
The temperature-dependent incompressible nematic liquid crystal flows in a bounded domain Ω⊂RN (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.
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