Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Injection-suction control for Navier-Stokes equations with slippage   We consider a velocity tracking problem for the Navier-Stokes equations in a
2D-bounded domain. The control acts on the boundary through a injection-suction
device and the flow is allowed to slip against the surface wall. We study the
well-posedness of the state equations, linearized state equations and adjoint
equations. In addition, we show the existence of an optimal solution and
establish the first order optimality condition.

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The categories of this paper are: hep-th
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The categories of this paper are: adap-org
1
The categories of this paper are: cs
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The categories of this paper are: nlin
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The categories of this paper are: q-bio
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The categories of this paper are: funct-an
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The categories of this paper are: q-fin
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The categories of this paper are: econ
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The categories of this paper are: comp-gas
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The categories of this paper are: physics
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The categories of this paper are: q-alg
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The categories of this paper are: gr-qc
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The categories of this paper are: cond-mat
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The categories of this paper are: astro-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-th