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

@inproceedings{Gerard2021OnSP, 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}, year={2021} }

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.

## One Citation

### Unconditional uniqueness for the Benjamin-Ono equation

- Mathematics
- 2021

We study the unconditional uniqueness of solutions to the Benjamin-Ono equation with initial data in H, both on the real line and on the torus. We use the gauge transformation of Tao and two…

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