Global regularity of the generalized liquid crystal model with fractional diffusion

Abstract

In this paper, we consider the global regularity for a n-dimensional generalized liquid crystal system with fractional diffusion term ζ2u for the velocity field, where ζuˆ(ξ)=|ξ|αg(|ξ|)uˆ(ξ) and g2(|ξ|)≤C0log⁡(e+|ξ|) for α≥1+n2. This paper provides a global regularity result for the generalized liquid crystal equations, which extends the result given by Jin, Zhu and Jin to the case β=0 for n=2 (Jin et al. (2015) [5]).