Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the stability in weak topology of the set of global solutions to the
  Navier-Stokes equations   Let $X$ be a suitable function space and let $\cG \subset X$ be the set of
divergence free vector fields generating a global, smooth solution to the
incompressible, homogeneous three dimensional Navier-Stokes equations. We prove
that a sequence of divergence free vector fields converging in the sense of
distributions to an element of $\cG$ belongs to $\cG$ if $n$ is large enough,
provided the convergence holds "anisotropically" in frequency space. Typically
that excludes self-similar type convergence. Anisotropy appears as an important
qualitative feature in the analysis of the Navier-Stokes equations; it is also
shown that initial data which does not belong to $\cG$ (hence which produces a
solution blowing up in finite time) cannot have a strong anisotropy in its
frequency support.

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The categories of this paper are: q-alg
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The categories of this paper are: solv-int
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The categories of this paper are: stat
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The categories of this paper are: econ
12
The categories of this paper are: nucl-th
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The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
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The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin
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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: ao-sci
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The categories of this paper are: alg-geom
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The categories of this paper are: comp-gas
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The categories of this paper are: eess