Well-Posedness of the Ericksen–Leslie System

被引：2

作者：

Wei Wang

Pingwen Zhang

Zhifei Zhang

机构：

[1] Peking University,School of Mathematical Sciences and Beijing International Center for Mathematical Research

[2] Peking University,School of Mathematical Sciences and LMAM

来源：

Archive for Rational Mechanics and Analysis | 2013年 / 210卷

关键词：

Liquid Crystal; Weak Solution; Nematic Liquid Crystal; Deborah Number; Leslie System;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We prove the local well-posedness of the Ericksen–Leslie system, and the global well-posedness for small initial data under a physical constraint condition on the Leslie coefficients, which ensures that the energy of the system is dissipated. Instead of the Ginzburg–Landau approximation, we construct an approximate system with the dissipated energy based on a new formulation of the system.

引用

页码：837 / 855

页数：18

共 50 条

[1] Well-Posedness of the Ericksen-Leslie System
Wang, Wei
Zhang, Pingwen
Zhang, Zhifei
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2013, 210 (03) : 837 - 855
[2] GLOBAL WELL-POSEDNESS FOR ERICKSEN-LESLIE SYSTEM WITH ZERO VISCOSITY
Zhou, Jianfeng
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2024, 152 (05) : 2185 - 2197
[3] WELL-POSEDNESS OF THE FULL ERICKSEN-LESLIE SYSTEM IN BOUNDED DOMAINS
Wang, Huaijie
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2024, 29 (10): : 3980 - 4001
[4] Local well-posedness to inhomogeneous Ericksen–Leslie system with general Leslie stress tensor
Huajun Gong
Jinkai Li
Chen Xu
Zeitschrift für angewandte Mathematik und Physik, 2017, 68
[5] Local well-posedness to inhomogeneous Ericksen-Leslie system with general Leslie stress tensor
Gong, Huajun
Li, Jinkai
Xu, Chen
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2017, 68 (01):
[6] On the General Ericksen–Leslie System: Parodi’s Relation, Well-Posedness and Stability
Hao Wu
Xiang Xu
Chun Liu
Archive for Rational Mechanics and Analysis, 2013, 208 : 59 - 107
[7] On global well-posedness and decay of 3D Ericksen-Leslie system
Zhao, Xiufang
Duan, Ning
AIMS MATHEMATICS, 2021, 6 (11): : 12660 - 12679
[8] On the General Ericksen-Leslie System: Parodi's Relation, Well-Posedness and Stability
Wu, Hao
Xu, Xiang
Liu, Chun
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2013, 208 (01) : 59 - 107
[9] Well-posedness of the full Ericksen-Leslie model of nematic liquid crystals
Coutand, D
Shkoller, S
COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 2001, 333 (10): : 919 - 924
[10] ON WELL-POSEDNESS OF ERICKSEN-LESLIE'S HYPERBOLIC INCOMPRESSIBLE LIQUID CRYSTAL MODEL
Jiang, Ning
Luo, Yi-Long
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2019, 51 (01) : 403 - 434

← 1 2 3 4 5 →