On the analytic Birkhoff normal form of the Benjamin-Ono equation and applications

2021/03/14 by P. Gérard, T. Kappeler, Gérard, P. +3 · 1 citation
Engineering · Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Waves and Solitons #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2103.07981

openalex publication_date 2021/03/14 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

In this paper we prove that the Benjamin-Ono equation admits an analytic Birkhoff normal form in an open neighborhood of zero in H^s₀(\T, \R) for any s>-1/2 where H^s₀(\T, \R) denotes the subspace of the Sobolev space H^s(\T, \R) of elements with mean 0. As an application we show that for any -1/2

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