A new blowup criterion of strong solutions to the two-dimensional equations of compressible nematic liquid crystal flows

被引：0

作者：

Liu, Yang ^{[1
,2
]}

Guo, Renying ^{[1
]}

Zhao, Weiwei ^{[3
,4
]}

机构：

[1] Changchun Normal Univ, Coll Math, Changchun, Peoples R China

[2] Jilin Univ, Sch Math, Changchun, Peoples R China

[3] Hainan Univ, Sch Sci, Haikou, Peoples R China

[4] Hainan Univ, Sch Sci, Haikou 570228, Peoples R China

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2024年 / 47卷 / 02期

关键词：

blowup criterion; Cauchy problem; compressible nematic liquid crystal flows; strong solutions; NAVIER-STOKES EQUATIONS; CLASSICAL-SOLUTIONS; GLOBAL EXISTENCE; CAUCHY-PROBLEM;

D O I：

10.1002/mma.9680

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we concern the Cauchy problem of two-dimensional (2D) compressible nematic liquid crystal flows with vacuum as far-field density. Under a geometric condition for the initial orientation field, we establish a blowup criterion in terms of the integrability of the density for strong solutions to the compressible nematic liquid crystal flows. This criterion generalizes previous results of compressible nematic liquid crystal flows with vacuum, which concludes the initial boundary problem and Cauchy problem.

引用

页码：742 / 761

页数：20

共 14 条

[1]

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

[2] 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

[3] On multi-dimensional compressible flows of nematic liquid crystals with large initial energy in a bounded domain [J].

Jiang, Fei ;

Jiang, Song ;

Wang, Dehua .

JOURNAL OF FUNCTIONAL ANALYSIS, 2013, 265 (12) :3369-3397

[4]

KATO T, 1986, P SYMP PURE MATH, V45, P1

[5] REMARKS OF GLOBAL WELLPOSEDNESS OF LIQUID CRYSTAL FLOWS AND HEAT FLOWS OF HARMONIC MAPS IN TWO DIMENSIONS [J].

Lei, Zhen ;

Li, Dong ;

Zhang, Xiaoyi .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2014, 142 (11) :3801-3810

[6] On local classical solutions to the Cauchy problem of the two-dimensional barotropic compressible Navier-Stokes equations with vacuum [J].

Li, Jing ;

Liang, Zhilei .

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2014, 102 (04) :640-671

[7] Global Existence of Classical Solutions with Large Oscillations and Vacuum to the Three-Dimensional Compressible Nematic Liquid Crystal Flows [J].

Li, Jinkai ;

Xu, Zhonghai ;

Zhang, Jianwen .

JOURNAL OF MATHEMATICAL FLUID MECHANICS, 2018, 20 (04) :2105-2145

[8]

Littlefield L.J., 1979, ADV LIQ CRYST, DOI DOI 10.1016/B978-0-12-025004-2.50008-9

[9]

Liu Y., arXiv

[10] STRONG SOLUTIONS TO CAUCHY PROBLEM OF 2D COMPRESSIBLE NEMATIC LIQUID CRYSTAL FLOWS [J].

Liu, Yang ;

Zheng, Sining ;

Li, Huapeng ;

Liu, Shengquan .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2017, 37 (07) :3921-3938

← 1 2 →