GLOBAL WELL-POSEDNESS FOR ERICKSEN-LESLIE SYSTEM WITH ZERO VISCOSITY

被引：0

作者：

Zhou, Jianfeng ^{[1
]}

机构：

[1] Hunan Univ, Sch Math, Changsha 410082, Peoples R China

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2024年 / 152卷 / 05期

基金：

中国国家自然科学基金;

关键词：

Ericksen-Leslie system; well-posedness; decay estimate; zero viscosity; LIQUID-CRYSTAL FLOWS; BLOW-UP CRITERION; ASYMPTOTIC-BEHAVIOR; WEAK SOLUTION; EXISTENCE; REGULARITY;

D O I：

10.1090/proc/16731

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the global well-posedness of the simplified EricksenLeslie system with zero viscosity on the periodic domain T2. Precisely, we prove the global existence and uniqueness of smooth solution to Ericksen-Leslie system if the initial data (u0, backward difference d0) is small in H4(T2) x H4(T2). Furthermore, we derive the time decay estimate of backward difference d in H1(T2).

引用

页码：2185 / 2197

页数：13

共 33 条

[1] Optimal Boundary Control of a Simplified Ericksen-Leslie System for Nematic Liquid Crystal Flows in 2D [J].

Cavaterra, Cecilia ;

Rocca, Elisabetta ;

Wu, Hao .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2017, 224 (03) :1037-1086

[2] Global weak solution and blow-up criterion of the general Ericksen-Leslie system for nematic liquid crystal flows [J].

Cavaterra, Cecilia ;

Rocca, Elisabetta ;

Wu, Hao .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2013, 255 (01) :24-57

[3] Global existence and regularity of solutions for active liquid crystals [J].

Chen, Gui-Qiang ;

Majumdar, Apala ;

Wang, Dehua ;

Zhang, Rongfang .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2017, 263 (01) :202-239

[4] Global well-posedness for the 3-D MHD equations with partial diffusion in the periodic domain [J].

Chen, Wenji ;

Zhang, Zhifei ;

Zhou, Jianfeng .

SCIENCE CHINA-MATHEMATICS, 2022, 65 (02) :309-318

[5]

Constantin Peter, 1988, Chicago Lectures in Math. Series

[6] ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO THE LIQUID CRYSTAL SYSTEM IN HM(R3) [J].

Dai, Mimi ;

Schonbek, Maria .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2014, 46 (05) :3131-3150

[7] Asymptotic Behavior of Solutions to Liquid Crystal Systems in R3 [J].

Dai, Mimi ;

Qing, Jie ;

Schonbek, Maria .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2012, 37 (12) :2138-2164

[8]

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

[9]

Grafakos Loukas, 2014, Graduate Texts in Mathematics, V249, DOI DOI 10.1007/978-1-4939-1194-3

[10]

Hineman JL, 2013, ARCH RATION MECH AN, V210, P177, DOI 10.1007/s00205-013-0643-7

← 1 2 3 4 →