Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the rate of convergence to equilibrium for the homogeneous Landau
  equation with soft potentials   We investigate in this work the rate of convergence to equilibrium of
solutions to the spatially homogeneous Landau equation with soft potentials.
Firstly, we prove a polynomial in time convergence using an entropy method with
some new a priori estimates. Finally we prove an exponential in time
convergence towards the equilibrium with the optimal rate given by the spectral
gap of the associated linearized operator, combining new decay estimates for
the semigroup generated by the linearized Landau operator in weighted
$L^p$-spaces togheter with the polynomial decay described above.

27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
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The categories of this paper are: eess
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ