Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stability of time-dependent Navier-Stokes flow and algebraic energy
  decay   Let $V$ be a given time-dependent Navier-Stokes flow of an incompressible
viscous fluid in the whole space ($n=3,4$). Assume such $V$ to be small in
$L^\infty(0,\infty; L^{n,\infty})$, where $L^{n,\infty}$ denotes the weak-$L^n$
space. The energy stability of this basic flow $V$ with respect to any initial
disturbance in $L^2_\sigma$ has been established by Karch, Pilarczyk and
Schonbek. In this paper we study, under reasonable conditions, the algebraic
rates of energy decay of disturbances as $t\to\infty$.

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The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
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The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
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The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
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The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: stat
18
The categories of this paper are: econ