GLOBAL WELL-POSEDNESS OF NON-ISOTHERMAL INHOMOGENEOUS NEMATIC LIQUID CRYSTAL FLOWS

被引：3

作者：

Bian, Dongfen ^{[1
,2
]}

Xiao, Yao ^{[3
]}

机构：

[1] Beijing Inst Technol, Sch Math & Stat, Beijing 100081, Peoples R China

[2] Beijing Inst Technol, Beijing Key Lab MCAACI, Beijing 100081, Peoples R China

[3] Chinese Univ Hong Kong, Inst Math Sci, Hong Kong, Peoples R China

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2021年 / 26卷 / 03期

关键词：

Nematic liquid crystal; strong solution; local solution; global solution; maximal regularity; inhomogeneous case; WEAK SOLUTIONS; VARIABLE VISCOSITY; EXISTENCE; MODEL; REGULARITY; UNIQUENESS; EQUATIONS; SYSTEM;

D O I：

10.3934/dcdsb.2020161

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider the initial-boundary value problem to the non-isothermal incompressible liquid crystal system with both variable density and temperature. Global well-posedness of strong solutions is established for initial data being small perturbation around the equilibrium state. As the tools in the proof, we establish the maximal regularities of the linear Stokes equations and parabolic equations with variable coefficients and a rigid lemma for harmonic maps on bounded domains. This paper also generalizes the result in [5] to the inhomogeneous case.

引用

页码：1243 / 1272

页数：30

共 48 条

[1] NONSTATIONARY STOKES SYSTEM WITH VARIABLE VISCOSITY IN BOUNDED AND UNBOUNDED DOMAINS [J].

Abels, Helmut .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, 2010, 3 (02) :141-157

[2] On Stokes operators with variable viscosity in bounded and unbounded domains [J].

Abels, Helmut ;

Terasawa, Yutaka .

MATHEMATISCHE ANNALEN, 2009, 344 (02) :381-429

[3]

Adams R. A., 2003, PURE APPL MATH AMSTE, VSecond, P140

[4]

Amann H., 1995, MONOGRAPHS MATH, V89

[5] Global solution to the nematic liquid crystal flows with heat effect [J].

Bian, Dongfen ;

Xiao, Yao .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2017, 263 (09) :5298-5329

[6] LP-theory for a class of non-newtonian fluids [J].

Bothe, Dieter ;

Pruess, Jan .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2007, 39 (02) :379-421

[7] Density-dependent incompressible fluids in bounded domains [J].

Danchin, R. .

JOURNAL OF MATHEMATICAL FLUID MECHANICS, 2006, 8 (03) :333-381

[8]

Denk R, 2003, MEM AM MATH SOC, V166, P1

[9] WEAK SOLUTION TO COMPRESSIBLE HYDRODYNAMIC FLOW OF LIQUID CRYSTALS IN DIMENSION ONE [J].

Ding, Shijin ;

Wang, Changyou ;

Wen, Huanyao .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2011, 15 (02) :357-371

[10]

DING WY, 1992, J PARTIAL DIFFERENTI, V5

← 1 2 3 4 5 →