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arXiv · 2109.00610

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

Patrick Gérard·Thomas Kappeler·Peter Topalov
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Abstract

We prove smoothing properties of the solutions of the Benjamin-Ono equation in the Sobolev space $H^{s}(\mathbb{T},\mathbb{R})$ for any $s\ge 0$. To this end we show that Tao's gauge transform is a high frequency approximation of the nonlinear Fourier transform $\Phi$ 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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Patrick Gérard, Thomas Kappeler, Peter Topalov. 2021-09-01. On smoothing properties and Tao's gauge transform of the Benjamin-Ono equation on the torus. https://arxiv.org/abs/2109.00610

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