On optimal boundary control of Ericksen-Leslie system in dimension two

被引：10

作者：

Liu, Qiao ^{[1
]}

Wang, Changyou ^{[2
]}

Zhang, Xiaotao ^{[3
]}

Zhou, Jianfeng ^{[4
]}

机构：

[1] Hunan Normal Univ, Coll Math & Stat, Key Lab High Performance Comp & Stochast Informat, Changsha 410081, Hunan, Peoples R China

[2] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA

[3] Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China

[4] Xiamen Univ, Sch Math Sci, Xiamen 361005, Fujian, Peoples R China

来源：

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2020年 / 59卷 / 01期

关键词：

LIQUID-CRYSTAL FLOWS; NAVIER-STOKES SYSTEM; SUFFICIENT CONDITIONS; WELL-POSEDNESS; WEAK SOLUTION; REGULARITY; EXISTENCE; UNIQUENESS; EVOLUTION; BEHAVIOR;

D O I：

10.1007/s00526-019-1676-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider the boundary value problem of a simplified Ericksen-Leslie system in dimension two with non-slip boundary condition for the velocity field u and time-dependent boundary condition for the director field d of unit length. For such a system, we first establish the existence of a global weak solution that is smooth away from finitely many singular times, then establish the existence of a unique global strong solution that is smooth for t > 0 under the assumption that the image of boundary data is contained in the hemisphere S-+(2). Finally, we apply these theorems to the problem of optimal boundary control of the simplified Ericksen-Leslie system and show both the existence and a necessary condition of an optimal boundary control.

引用

页数：64

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