Global existence of solutions to the 2D incompressible liquid crystal flow with fractional diffusion

Abstract

In this paper, we consider the global regularity for 2D liquid crystal model with fractional diffusion. Global regularity is proved for two cases: 0 < β < 1, α + β = 2 or β = 1, α > 0.

On Regularity Criteria for the Two-Dimensional Generalized Liquid Crystal Model

“…In [10], Fan et al established a global regularity for this system with mixed partial viscosity. Recently, in [11,12], it is proved that smooth solutions are global in the following three cases: 0 < < 1, + ≥ 2; > 0, = 1; = 0, > 1. Moreover, global strong solution to the density-dependent 2D liquid crystal flows was studied in [13].…”