Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Invariant measure and long time behavior of regular solutions of the
  Benjamin-Ono equation   The Benjamin-Ono equation describes the propagation of internal waves in a
stratified fluid. In the present work, we study large time dynamics of its
regular solutions via some probabilistic point of view. We prove the existence
of an invariant measure concentrated on $C^\infty(\T)$ and establish some
qualitative properties of this measure. We then deduce a recurrence property of
regular solutions and other corollaries using ergodic theorems. The approach
used in this paper applies to other equations with infinitely many conservation
laws, such as the KdV and cubic Schr\"odinger equations in 1D. It uses the
fluctuation-dissipation-limit approach and relies on a \textit{uniform}
smoothing lemma for stationary solutions to the damped-driven Benjamin-Ono
equation.

12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat