Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global-in-time L p -- L q estimates for solutions of the
  Kramers-Fokker-Planck equation   In this work, we prove an optimal global-in-time L p --L q estimate for
solutions to the Kramers-Fokker-Planck equation with short range potential in
dimension three. Our result shows that the decay rate as t $\rightarrow$
+$\infty$ is the same as the heat equation in x-variables and the divergence
rate as t $\rightarrow$ 0 + is related to the sub-ellipticity with loss of 1/3
derivatives of the Kramers-Fokker-Planck operator.

28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph
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The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
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The categories of this paper are: q-fin
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The categories of this paper are: ao-sci
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The categories of this paper are: solv-int
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The categories of this paper are: hep-lat
3
The categories of this paper are: physics
16
The categories of this paper are: stat
9
The categories of this paper are: nlin