Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Strong Convergence to Equilibrium for the Boltzmann Equation with
  Soft Potentials   The paper concerns $L^1$- convergence to equilibrium for weak solutions of
the spatially homogeneous Boltzmann Equation for soft potentials $(-4\le
\gm<0$), with and without angular cutoff. We prove the time-averaged
$L^1$-convergence to equilibrium for all weak solutions whose initial data have
finite entropy and finite moments up to order greater than $2+|\gm|$. For the
usual $L^1$-convergence we prove that the convergence rate can be controlled
from below by the initial energy tails, and hence, for initial data with long
energy tails, the convergence can be arbitrarily slow. We also show that under
the integrable angular cutoff on the collision kernel with $-1\le \gm<0$, there
are algebraic upper and lower bounds on the rate of $L^1$-convergence to
equilibrium. Our methods of proof are based on entropy inequalities and moment
estimates.

35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
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The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
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The categories of this paper are: alg-geom
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The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
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The categories of this paper are: eess
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex