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

Patrick Gérard, Thomas Kappeler, Peter Topalov

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 gau…