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

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arxiv 1811.03512 v1 pith:AGSS3JBB submitted 2018-11-08 math.AP

classification math.AP
keywords boundarysystemconditioncontrolericksen-leslieexistenceoptimaldimension
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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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  1. Global well-posedness of magnetohydrodynamic equations

    math.AP 2019-08 conditional novelty 5.0 of 10

    Global weak solutions for 2D and 3D MHD with time-dependent magnetic boundary data, with 2D strong solutions and a uniform attractor.

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