In this paper, a macromolecular non-isothermal model for the incompressible
hydrodynamics flow of nematic liquid crystals on T3 is considered. By a Galerkin
approximation, we prove the local existence of a unique strong solution if the initial
data u0, d0 and θ0 satisfy some natural conditions and provided that the viscosity
coefficients μ and the heat conductivity κ, h, which are temperature dependent, are
properly differentiable and bounded. Moreover, with small initial data, we can extend
the local strong solution to be a global one by the argument of contradiction. In this
case, the exponential time decay rate is also established.

EB00000003128K

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• Global well-posedness of the non-isothermal model for incompressible nematic liquid crystals