数学物理学报 ›› 2020, Vol. 40 ›› Issue (4): 918-924.

• 论文 • 上一篇    下一篇

分数阶扩散的三维液晶方程的整体正则性

李强()   

  1. 河南理工大学数学与信息科学学院 河南焦作 454000
  • 收稿日期:2019-06-20 出版日期:2020-08-26 发布日期:2020-08-20
  • 作者简介:李强, E-mail:1220494943@qq.com

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

摘要:

该文考虑的是带有分数阶耗散项$(-\Delta)^{\alpha}u$$(-\Delta)^{\beta}d$的广义不可压缩液晶模型.目标是在需要最小的耗散情况下建立整体正则性.在初值充分光滑的情况下,若耗散指标$\alpha\geq\frac{5}{4}$, $\beta\geq\frac{5}{4}$,方程组有唯一的整体光滑解.

关键词: 液晶方程, 分数阶耗散, 整体正则性

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

中图分类号: 

  • O175.29