Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimal boundary control of a simplified Ericksen--Leslie system for
  nematic liquid crystal flows in $2D$   In this paper, we investigate an optimal boundary control problem for a two
dimensional simplified Ericksen--Leslie system modelling the incompressible
nematic liquid crystal flows. The hydrodynamic system consists of the
Navier--Stokes equations for the fluid velocity coupled with a convective
Ginzburg--Landau type equation for the averaged molecular orientation. The
fluid velocity is assumed to satisfy a no-slip boundary condition, while the
molecular orientation is subject to a time-dependent Dirichlet boundary
condition that corresponds to the strong anchoring condition for liquid
crystals. We first establish the existence of optimal boundary controls. Then
we show that the control-to-state operator is Fr\'echet differentiable between
appropriate Banach spaces and derive first-order necessary optimality
conditions in terms of a variational inequality involving the adjoint state
variables.

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The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
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The categories of this paper are: q-alg
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The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
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The categories of this paper are: stat
9
The categories of this paper are: nlin
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The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
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The categories of this paper are: comp-gas
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The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
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The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc