Dynamics and Flow Effects in the Beris-Edwards System Modeling Nematic Liquid Crystals

被引：22

作者：

Wu, Hao ^{[1
,2
,3
]}

Xu, Xiang ^{[4
]}

Zarnescu, Arghir ^{[5
,6
,7
]}

机构：

[1] Fudan Univ, Sch Math Sci, Han Dan Rd 220, Shanghai 200433, Peoples R China

[2] Fudan Univ, Shanghai Key Lab Contemporary Appl Math, Han Dan Rd 220, Shanghai 200433, Peoples R China

[3] Fudan Univ, Minist Educ, Key Lab Math Nonlinear Sci, Han Dan Rd 220, Shanghai 200433, Peoples R China

[4] Old Dominion Univ, Dept Math & Stat, Norfolk, VA 23529 USA

[5] Ikerbasque, Basque Fdn Sci, Maria Diaz de Haro 3, Bilbao 48013, Bizkaia, Spain

[6] BCAM, Mazarredo 14, E-48009 Bilbao, Bizkaia, Spain

[7] Romanian Acad, Simion Stoilow Inst, 21 Calea Grivitei, Bucharest 010702, Romania

来源：

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS | 2019年 / 231卷 / 02期

关键词：

Q-TENSOR SYSTEM; COUPLED NAVIER-STOKES; WEAK SOLUTIONS; REGULARITY; UNIQUENESS; EXISTENCE;

D O I：

10.1007/s00205-018-1297-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the Beris-Edwards system modelling incompressible liquid crystal flows of nematic type. This couples a Navier-Stokes system for the fluid velocity with a parabolic reaction-convection-diffusion system for the Q-tensors describing the average orientation of liquid crystal molecules. In this paper, we study the effect that the flow has on the dynamics of the Q-tensors by considering two fundamental aspects: the preservation of the eigenvalue-range and the dynamical emergence of defects in the limit of large Ericksen number.

引用

页码：1217 / 1267

页数：51

共 48 条

[1] On partial regularity criterion for the co-rotational Beris-Edwards system modeling nematic liquid crystal flow [J].

Liu, Qiao .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2021, 301 :300-329

[2] STRONG SOLUTIONS FOR THE BERIS-EDWARDS MODEL FOR NEMATIC LIQUID CRYSTALS WITH HOMOGENEOUS DIRICHLET BOUNDARY CONDITIONS [J].

Abels, Helmut ;

Dolzmann, Georg ;

Liu, YuNing .

ADVANCES IN DIFFERENTIAL EQUATIONS, 2016, 21 (1-2) :109-152

[3] Boundary layers for the upper-convected Beris-Edwards model of nematic liquid crystals [J].

De Anna, Francesco ;

Kortum, Joshua ;

Zarnescu, Arghir .

NONLINEARITY, 2025, 38 (04)

[4] Number of Singular Points and Energy Equality for the Co-rotational Beris-Edwards System Modeling Nematic Liquid Crystal Flow [J].

Liu, Qiao .

JOURNAL OF MATHEMATICAL FLUID MECHANICS, 2023, 25 (03)

[5] Global Existence of Strong Solutions for Beris-Edwards's Liquid Crystal System in Dimension Three [J].

Luo, Yongshun ;

Li, Sirui ;

Zhao, Fangxin .

MATHEMATICS, 2019, 7 (10)

[6] Long-Time Behavior of Global Weak Solutions for a Beris-Edwards Type Model of Nematic Liquid Crystals [J].

Climent-Ezquerra, Blanca ;

Guillen-Gonzalez, Francisco .

JOURNAL OF MATHEMATICAL FLUID MECHANICS, 2022, 24 (04)

[7] Global well-posedness of the two dimensional Beris-Edwards system with general Laudau-de Gennes free energy [J].

Liu, Yuning ;

Wu, Hao ;

Xu, Xiang .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2019, 267 (12) :6958-7001

[8] THE HYDROSTATIC LIMIT OF THE BERIS-EDWARDS SYSTEM IN DIMENSION TWO [J].

Li, Xingyu ;

Paicu, Marius ;

Zarnescu, Arghir .

COMMUNICATIONS IN MATHEMATICAL SCIENCES, 2024, 22 (06) :1701-1732

[9] Suitable Weak Solutions for the Co-rotational Beris-Edwards System in Dimension Three [J].

Du, Hengrong ;

Hu, Xianpeng ;

Wang, Changyou .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2020, 238 (02) :749-803

[10] On partial regularity for weak solutions to the 3D co-rotational Beris-Edwards system [J].

Liu, Qiao .

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2023, 71

← 1 2 3 4 5 →