Gaussian measures associated to the higher order conservation laws of the Benjamin-Ono equation
arXiv:1109.5291
Abstract
Inspired by the work of Zhidkov on the KdV equation, we perform a construction of weighted gaussian measures associated to the higher order conservation laws of the Benjamin-Ono equation. The resulting measures are supported by Sobolev spaces of increasing regularity. We also prove a property on the support of these measures leading to the conjecture that they are indeed invariant by the flow of the Benjamin-Ono equation.
arXiv comment51 pages, revised version to appear on Annales E.N.S