Acta mathematica scientia,Series A ›› 2020, Vol. 40 ›› Issue (4): 918-924.

Previous Articles     Next Articles

Global Regularity for the 3D Liquid Crystal Equations with Fractional Diffusion

Qiang Li()   

  1. School of Mathematics and Information Science, Henan Polytechnic University, Henan Jiaozuo 454000
  • Received:2019-06-20 Online:2020-08-26 Published:2020-08-20

Abstract:

In this paper, the focus is the global regularity of three-dimensional liquid crystal equations with fractional dissipations $(-\Delta)^{\alpha}u$ and $(-\Delta)^{\beta}d$. The objective is to establish the global regularity of the fractional liquid crystal equations with the minimal amount of dissipations. And it is obtained that the equations have a global classical solution with sufficiently smooth data if $\alpha\geq\frac{5}{4}$ and $\beta\geq\frac{5}{4}$.

Key words: Liquid crystal equations, Fractional dissipation, Global regularity

CLC Number: 

  • O175.29
Trendmd