• Corpus ID: 237385829

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

  title={On smoothing properties and Tao's gauge transform of the Benjamin-Ono equation on the torus},
  author={Patrick G'erard and Thomas Kappeler and Peter Topalov},
We prove smoothing properties of the solutions of the Benjamin-Ono equation in the Sobolev space Hs(T,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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