The Ericksen-Leslie System for Data on a Plane

被引：0
|
作者：
Barbera, Daniele [1 ]
Georgiev, Vladimir [1 ,2 ,3 ]
机构：
[1] Univ Pisa, Dipartimento Matemat, Largo B Pontecorvo 5, I-56100 Pisa, Italy
[2] Waseda Univ, Fac Sci & Engn, 3-4-1 Okubo,Shinjuku Ku, Tokyo 1698555, Japan
[3] Bulgarian Acad Sci, Inst Math & Informat, Acad Georgi Bonchev Str,Block 8, Sofia 1113, Bulgaria
来源：
NEW TRENDS IN THE APPLICATIONS OF DIFFERENTIAL EQUATIONS IN SCIENCES, NTADES 2023 | 2024年 / 449卷
关键词：
Liquid crystals; Ericksen-Leslie; Heat equation; Stokes equation; Energy estimates; NEMATIC LIQUID-CRYSTALS; GLOBAL EXISTENCE; REGULARITY; DECAY; FLOW;
D O I：
10.1007/978-3-031-53212-2_8
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The work deals with the Ericksen-Leslie system for nematic liquid crystals on the whole space with dimension greater or equal than 3. In our work we suppose the initial condition of the orientation field stays on an arc connecting two fixed orthogonal vectors on the unit sphere. Thanks to this geometric assumption, we prove through energy a priori estimates the local existence and the global existence with decay in time for small initial data of a solution in Sobolev spaces asking low regularity for the initial conditions.
引用
收藏
页码：95 / 106
页数：12
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