Global Strong Solutions to the Compressible Nematic Liquid Crystal Flows with Large Oscillations and Vacuum in 2D Bounded Domains

被引：1

作者：

Sun, Yimin ^{[1
]}

Zhong, Xin ^{[1
]}

机构：

[1] Southwest Univ, Sch Math & Stat, Chongqing 400715, Peoples R China

来源：

JOURNAL OF GEOMETRIC ANALYSIS | 2023年 / 33卷 / 10期

关键词：

Compressible nematic liquid crystal flows; Global strong solutions; Navier-slip boundary conditions; Large oscillations; LARGE-TIME BEHAVIOR; WEAK SOLUTIONS; EXISTENCE; EQUATIONS; ENERGY;

D O I：

10.1007/s12220-023-01386-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We investigate a simplified compressible nematic liquid crystal flow in two-dimensional (2D) bounded domains with Navier slip boundary conditions for velocity and Neumann boundary condition for orientation field. Based on delicate energy method and the structure of the model under consideration, we show the global existence and uniqueness of strong solutions when the initial total energy is suitably small. Our result may be regarded as an extension of the 2D Cauchy problem due to Wang (J Math Fluid Mech 18(3):539-569, 2016).

引用

页数：44

共 30 条

[1]

[Anonymous], 1996, Discrete and Continuous Dynamical Systems, DOI [DOI 10.3934/dcds.1996.2.1, DOI 10.3934/DCDS.1996.2.1]

[2]

Aramaki J., 2014, International Journal of Mathematics and Analysis, V8, P259

[3]

Cao Y, ARXIV

[4]

ERICKSEN JL, 1962, ARCH RATION MECH AN, V9, P371

[5]

Evans L.C., 2010, Partial Differential Equations

[6]

Gong HJ, 2020, COMMUN MATH SCI, V18, P1891

[7]

Hieber M, 2018, Handbook of mathematical analysis in mechanics of viscous fluids, P1075

[8] GLOBAL SOLUTION TO THE THREE-DIMENSIONAL COMPRESSIBLE FLOW OF LIQUID CRYSTALS [J].

Hu, Xianpeng ;

Wu, Hao .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2013, 45 (05) :2678-2699

[9] Strong solutions of the compressible nematic liquid crystal flow [J].

Huang, Tao ;

Wang, Changyou ;

Wen, Huanyao .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2012, 252 (03) :2222-2265

[10] Global Weak Solutions to the Equations of Compressible Flow of Nematic Liquid Crystals in Two Dimensions [J].

Jiang, Fei ;

Jiang, Song ;

Wang, Dehua .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2014, 214 (02) :403-451

← 1 2 3 →