Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Strongly Compact Strong Trajectory Attractors for Evolutionary Systems
  and their Applications   We show that for any fixed accuracy and time length $T$, a finite number of
$T$-time length pieces of the complete trajectories on the global attractor are
capable of uniformly approximating all trajectories within the accuracy in the
natural strong metric after sufficiently large time when the observed
dissipative system is asymptotically compact. Moreover, we obtain the strong
equicontinuity of all the complete trajectories on the global attractor. These
results follow by proving the existence of a notion of a strongly compact
strong trajectory attractor. The notion of a (weak) trajectory attractor was
previously established for a system without uniqueness by considering a family
of auxiliary systems including the original one. Recently, Cheskidov and the
author developed a new framework called evolutionary system, with which a
(weak) trajectory attractor can be defined for the original system under
consideration. In this paper, the theory of trajectory attractors is further
developed for our purpose, where the trajectory attractor plays a new role. We
then apply it to both the 2D and the 3D Navier-Stokes equations and a general
nonautonomous reaction-diffusion system. Global attractors are ever anticipated
to be very complicated objects, which obstruct their applications. We expect
that our results will do some good for their practical utilization, for
instance for numerical simulations.

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The categories of this paper are: astro-ph
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: bayes-an
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: alg-geom
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The categories of this paper are: econ
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The categories of this paper are: eess
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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: physics
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The categories of this paper are: hep-th
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The categories of this paper are: stat