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arXiv · 1811.03512

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

Qiao Liu·Changyou Wang·Xiaotao Zhang·Jianfeng Zhou
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Abstract

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 $\mathbb S^2_+$. 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.

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Qiao Liu, Changyou Wang, Xiaotao Zhang, Jianfeng Zhou. 2018-11-08. On optimal boundary control of Ericksen-Leslie system in dimension two. https://arxiv.org/abs/1811.03512

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