On smoothing properties and Tao's gauge transform of the Benjamin-Ono equation on the torus

2021/09/01 by Patrick Gérard, Gérard, Patrick, Thomas Kappeler +3 · 2 citations
Mathematics · Physics and Astronomy · #37K15 #47B35 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Waves and Solitons #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2109.00610

openalex publication_date 2021/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove smoothing properties of the solutions of the Benjamin-Ono equation in the Sobolev space H^s(\mathbbT,ℝ) for any s≥ 0. To this end we show that Tao's gauge transform is a high frequency approximation of the nonlinear Fourier transform Φ for the Benjamin-Ono equation, constructed in our previous work. The results of this paper are manifestations of the quasi-linear character of the Benjamin-Ono equation.

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