| 概要 | The KdV and the Benjamin-Ono equations are basic models,
derived from the water waves equations for the propagation
of long, small amplitude one dimensional waves. The
solutions of the KdV equations, posed on the torus are
known to be almost periodic in time. The long time
behavior of the Benjamin-Ono equation, posed on the torus
is much less understood. In this talk, we will present
some progress on this problem. Namely, we shall construct
an infinite sequence of weighted gaussian measures which
are invariant by the flow of the Benjamin-Ono equation.
These measures are supported by Sobolev spaces of
increasing regularities. The "probabilistic view point" is
essential in our analysis. In particular our arguments are
less dependent on the particular behavior of each
trajectory, compared to previous works on the subject. The
talk is based on a series of joint works with Nicola Visciglia. |