Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Continuous Data Assimilation for the 2D B\'enard Convection through
  Velocity Measurements Alone   An algorithm for continuous data assimilation for the two- dimensional
B\'enard convection problem is introduced and analyzed. It is inspired by the
data assimilation algorithm developed for the Navier-Stokes equations, which
allows for the implementation of variety of observables: low Fourier modes,
nodal values, finite volume averages, and finite elements. The novelty here is
that the observed data is obtained for the velocity field alone; i.e. no
temperature measurements are needed for this algorithm. We provide conditions
on the spatial resolution of the observed data, under the assumption that the
observed data is free of noise, which are sufficient to show that the solution
of the algorithm approaches, at an exponential rate, the unique exact unknown
solution of the B\'enard convection problem associated with the observed
(finite dimensional projection of) velocity.

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The categories of this paper are: physics
32
The categories of this paper are: atom-ph
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The categories of this paper are: econ
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The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ph
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The categories of this paper are: stat
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The categories of this paper are: q-bio
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The categories of this paper are: ao-sci
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The categories of this paper are: chao-dyn
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The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
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The categories of this paper are: cs
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The categories of this paper are: dg-ga
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The categories of this paper are: cond-mat