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

Abstract

In this paper, a macromolecular non-isothermal model for the incompressible hydrodynamics flow of nematic liquid crystals on mathbb {T}^{3} is considered. By a Galerkin approximation, we prove the local existence of a unique strong solution if the initial data u_{0}, d_{0} and theta_{0} 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.