On the analyticity of the nonlinear Fourier transform of the Benjamin-Ono equation on \mathbbT

2021/09/18 by Gérard, P., Kappeler, T., Topalov, P. · 1 citation
#37K15 #47B35 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2109.08988

Abstract

We prove that the nonlinear Fourier transform of the Benjamin-Ono equation on \mathbbT, also referred to as Birkhoff map, is a real analytic diffeomorphism from the scale of Sobolev spaces H^s₀(\mathbbT,ℝ), s > -1/2, to the scale of weighted ℓ²-sequence spaces, \mathfrakh^{s +1/2}_r,0(ℕ,ℂ), s >-1/2. As an application we show that for any -1/2

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• Global well-posedness for the ILW equation in H^s(\mathbbT) for s>-\frac12

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