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 . 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 .
Cite this article
Yu Deng, Invariance of the Gibbs measure for the Benjamin–Ono equation. J. Eur. Math. Soc. 17 (2015), no. 5, pp. 1107–1198DOI 10.4171/JEMS/528