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 39 条

[21] UNIQUENESS OF WEAK SOLUTIONS OF THE FULL COUPLED NAVIER-STOKES AND Q-TENSOR SYSTEM IN 2D [J].

De Anna, Francesco ;

Zarnescu, Arghir .

COMMUNICATIONS IN MATHEMATICAL SCIENCES, 2016, 14 (08) :2127-2178

[22] PARTIAL REGULARITY FOR MINIMIZERS OF SINGULAR ENERGY FUNCTIONALS, WITH APPLICATION TO LIQUID CRYSTAL MODELS [J].

Evans, Lawrence C. ;

Kneuss, Olivier ;

Hung Tran .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2016, 368 (05) :3389-3413

[23] Higher order commutator estimates and local existence for the non-resistive MHD equations and related models [J].

Fefferman, Charles L. ;

McCormick, David S. ;

Robinson, James C. ;

Rodrigo, Jose L. .

JOURNAL OF FUNCTIONAL ANALYSIS, 2014, 267 (04) :1035-1056

[24] Nonisothermal nematic liquid crystal flows with the Ball-Majumdar free energy [J].

Feireisl, Eduard ;

Schimperna, Giulio ;

Rocca, Elisabetta ;

Zarnescu, Arghir .

ANNALI DI MATEMATICA PURA ED APPLICATA, 2015, 194 (05) :1269-1299

[25]

Feireisl E, 2014, COMMUN MATH SCI, V12, P317

[26] Weak solutions for an initial-boundary Q-tensor problem related to liquid crystals [J].

Guillen-Gonzalez, Francisco ;

Angeles Rodirguez-Bellido, Maria .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2015, 112 :84-104

[27] WEAK TIME REGULARITY AND UNIQUENESS FOR A Q-TENSOR MODEL [J].

Guillen-Gonzalez, Francisco ;

Angeles Rodriguez-Bellido, Maria .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2014, 46 (05) :3540-3567

[28]

Hartman P., 1982, Ordinary Differential Equations

[29] Dynamic cubic instability in a 2D Q-tensor model for liquid crystals [J].

Iyer, Gautam ;

Xu, Xiang ;

Zarnescu, Arghir D. .

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2015, 25 (08) :1477-1517

[30] COMMUTATOR ESTIMATES AND THE EULER AND NAVIER-STOKES EQUATIONS [J].

KATO, T ;

PONCE, G .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1988, 41 (07) :891-907

← 1 2 3 4 →