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

Abstract

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

Keywords

• incompressible flow
• nematic liquid crystals
• non-isothermal
• a priori estimates
• local and global existence and uniqueness