Global regularity for the incompressible 2D generalized liquid crystal model with fractional diffusions

In this paper, we consider the global regularity for the 2D generalized liquid crystal model with the fractional diffusion term − Λ 2 α u for the velocity field and − Λ 2 β d for the vector field modeling the orientation of the crystal molecules. Global existence of smooth solutions is proved for the case α = 0 , β > 1 .