2012/07/05 by Nikolay Tzvetkov, Nicola Visciglia, Tzvetkov, Nikolay +1
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Photonic Systems #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.1207.1175
openalex publication_date 2012/07/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the Benjamin-Ono equation, posed on the torus. We prove that an infinite sequence of weighted gaussian measures, constructed in our previous work, are invariant by the flow of the equation. These measures are supported by Sobolev spaces of increasing regularities. As a by product we deduce informations on the long time behaviour of regular solutions. To our knowledge this is the first result which gives an evidence about recurrence properties of the Benjamin-Ono equation flow.