Integrability and diffeomorphisms on target space.
Invariance of the Gibbs measure for the Benjamin–Ono equation
In this paper we consider the periodic Benjemin-Ono equation.We establish the invariance of the Gibbs measure associated to this equation, thus answering a question raised in Tzvetkov [28]. As an intermediate step, we also obtain a local well-posedness result in Besov-type spaces rougher than , extending the well-posedness result of Molinet [20].
Invariant measures for the defocusing Nonlinear Schrödinger equation
We prove the existence and the invariance of a Gibbs measure associated to the defocusing sub-quintic Nonlinear Schrödinger equations on the disc of the plane . We also prove an estimate giving some intuition to what may happen in dimensions.