具有大速度的三维非匀质不可压向列相液晶方程的全局适定性

数学物理学报 ›› 2026, Vol. 46 ›› Issue (3): 996-1014.

具有大速度的三维非匀质不可压向列相液晶方程的全局适定性

陈冬香(), 何倩(), 陈晓莉^*()

江西师范大学数学与统计学院南昌 330022

收稿日期:2025-03-14 修回日期:2025-10-21 出版日期:2026-06-26 发布日期:2026-06-16
通讯作者: 陈晓莉 E-mail:chendx020@163.com;248536440@qq.com;littleli_chen@163.com
作者简介:陈冬香, E-mail:chendx020@163.com;
何倩, E-mail:248536440@qq.com
基金资助:
国家自然科学基金(12461017);国家自然科学基金(12471016);江西省自然科学基金(20232BAB201014)

Global Well-Posedness of the Three-Dimensional Inhomogeneous Incompressible Nematic Liquid Crystal System with a Class of Large Velocity

Dongxiang Chen(), Qian He(), Xiaoli Chen^*()

School of Mathematics and Statistics, Jiangxi Normal University, Nanchang 330022

Received:2025-03-14 Revised:2025-10-21 Online:2026-06-26 Published:2026-06-16
Contact: Xiaoli Chen E-mail:chendx020@163.com;248536440@qq.com;littleli_chen@163.com
Supported by:
NSFC(12461017);NSFC(12471016);National Science Foundation of Jiangxi Province(20232BAB201014)

摘要/Abstract

摘要：

该文研究了一类具有大速度的三维不可压缩非匀质的向列相液晶方程的全局适定性问题. 具体地, 假设初值 $a_0\in\dot B_{p,1}^{\frac{3}{p}}, u_0\in\dot B_{p,1}^{\frac{3}{p}-1}, d_0\in\dot B_{p,1}^{\frac{3}{p}}$ 且满足

$C_{0}\left[\left\|u_{0}^{h}\right\|_{\dot{B}_{p, 1}^{\frac{3}{p}-1}}+\left(\left\|u_{0}^{3}\right\|_{\dot{B}_{p, 1}^{\frac{3}{p}-1}}+1\right)\left(\left\|a_{0}\right\|_{\dot{B}_{p, 1}^{\frac{3}{p}}}+\left\|d_{0}\right\|_{\dot{B}_{p, 1}^{\frac{3}{p}}}\right)\right] \exp \left\{C_{0}\left\|u_{0}^{3}\right\|_{\dot{B}_{p, 1}^{\frac{3}{p}-1}}^{2}\right\} \leq 1,$

则向列相液晶方程有唯一全局解, 其中 $C_0>0,~ 2\le p\le4.$

关键词: 向列相液晶方程, 大初值, 全局适定性, 垂直方向.

Abstract:

{In this paper, we investigate the the global well-posedness problem of the three-dimensional inhomogeneous incompressible nematic liquid crystal system with a class of large velocity. More precisely, assuming that the initial data $a_0\in\dot B_{p,1}^{\frac{3}{p}}, u_0\in\dot B_{p,1}^{\frac{3}{p}-1}, d_0\in\dot B_{p,1}^{\frac{3}{p}}$ satisfies

then the nematic liquid crystal equation admits a unique global solution, where $C_0>0,~ 2\le p\le4.$

Key words: nematic liquid crystal system, large initial data, global well-posedness, vertical direction.

中图分类号:

O175.26

陈冬香, 何倩, 陈晓莉. 具有大速度的三维非匀质不可压向列相液晶方程的全局适定性[J]. 数学物理学报, 2026, 46(3): 996-1014.

Dongxiang Chen, Qian He, Xiaoli Chen. Global Well-Posedness of the Three-Dimensional Inhomogeneous Incompressible Nematic Liquid Crystal System with a Class of Large Velocity[J]. Acta mathematica scientia,Series A, 2026, 46(3): 996-1014.

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