Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lyapunov Functionals and Local Dissipativity for the Vorticity Equation
  in L^p and Besov Spaces   In this paper we establish the local Lyapunov property of certain L^p and
Besov norms of the vorticity fields. We have resolved in part, a certain open
problem posed by Tosio Kato for the three dimensional Navier Stokes equation by
studying the vorticity equation. The local dissipativity of the sum of linear
and non-linear operators of the vorticity equation is established. One of the
main techniques used here is Littlewood-Paley analysis.

7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
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The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
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The categories of this paper are: solv-int
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The categories of this paper are: q-fin
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The categories of this paper are: chao-dyn
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The categories of this paper are: astro-ph
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The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
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The categories of this paper are: nlin
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The categories of this paper are: acc-phys