Construction of a Gibbs measure associated to the periodic Benjamin-Ono equation

Details Construction of a Gibbs measure associated to the periodic Benjamin-Ono equation Construction of a Gibbs measure associated to the periodic Benjamin-Ono equation

2006-10-20

arxiv.org/abs/math/0610626v2

Mathematics

Analysis of PDEs

To appear in Probability Theory and Related Fields

Scientific paper

We define a finite Borel measure of Gibbs type, supported by the Sobolev
spaces of negative indexes on the circle. The measure can be seen as a limit of
finite dimensional measures. These finite dimensional measures are invariant by
the ODE's which correspond to the projection of the Benjamin-Ono equation,
posed on the circle, on the first N>>1 modes in the trigonometric bases.

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