Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: What is the optimal shape of a pipe?   We consider an incompressible fluid in a three-dimensional pipe, following
the Navier-Stokes system with classical boundary conditions. We are interested
in the following question: is there any optimal shape for the criterion "energy
dissipated by the fluid"? Moreover, is the cylinder the optimal shape? We prove
that there exists an optimal shape in a reasonable class of admissible domains,
but the cylinder is not optimal. For that purpose, we explicit the first order
optimality condition, thanks to adjoint state and we prove that it is
impossible that the adjoint state be a solution of this over-determined system
when the domain is the cylinder. At last, we show some numerical simulations
for that problem.

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The categories of this paper are: supr-con
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The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
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The categories of this paper are: stat
24
The categories of this paper are: dg-ga
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The categories of this paper are: cmp-lg
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The categories of this paper are: plasm-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: chem-ph
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The categories of this paper are: q-fin
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The categories of this paper are: hep-lat
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The categories of this paper are: gr-qc
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The categories of this paper are: patt-sol
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The categories of this paper are: solv-int
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The categories of this paper are: eess