# Unconditional uniqueness for the Benjamin-Ono equation

@inproceedings{Mosincat2021UnconditionalUF, title={Unconditional uniqueness for the Benjamin-Ono equation}, author={Razvan O. Mosincat and Didier Pilod}, year={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 iterations of normal form reductions via integration by parts in time. By employing a refined Strichartz estimate we establish the result below the regularity threshold s = 1/6. As a by-product of our proof, we also obtain a nonlinear smoothing property on the gauge variable at the same level of regularity.

## One Citation

Unconditional well-posedness for some nonlinear periodic one-dimensional dispersive equations

- MathematicsJournal of Functional Analysis
- 2022

## References

SHOWING 1-10 OF 72 REFERENCES

Unconditional uniqueness for the periodic modified Benjamin–Ono equation by normal form approach

- Mathematics
- 2021

We show unconditional uniqueness of solutions to the Cauchy problem associated with the Benjamin-Ono equation under the periodic boundary condition with initial data given in $H^s$ for $s>1/6$. This…

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

- Mathematics
- 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…

The Benjamin—Ono equation in energy space

- Mathematics
- 2006

We prove existence of solutions for the Benjamin—Ono equation with data in H s(ℝ), s > 0. Thanks to conservation laws, this yields global solutions for H 1 2 (ℝ) data, which is the natural “finite…

Nonlinear smoothing and unconditional uniqueness for the Benjamin–Ono equation in weighted Sobolev spaces

- Mathematics
- 2020

Low regularity conservation laws for the Benjamin–Ono equation

- Mathematics, Physics
- 2018

We obtain conservation laws at negative regularity for the Benjamin-Ono equation on the line and on the circle. These conserved quantities control the $H^s$ norm of the solution for $-\frac{1}{2} < s…

On the Integrability of the Benjamin‐Ono Equation on the Torus

- MathematicsCommunications on Pure and Applied Mathematics
- 2020

In this paper we prove that the Benjamin‐Ono equation, when considered on the torus, is an integrable (pseudo)differential equation in the strongest possible sense: this equation admits global…

Unconditional uniqueness for the derivative nonlinear Schrödinger equation on the real line

- Mathematics
- 2018

We prove the unconditional uniqueness of solutions to the derivative nonlinear Schr\"odinger equation (DNLS) in an almost end-point regularity. To this purpose, we employ the normal form method and…

Ill-Posedness Issues for the Benjamin-Ono and Related Equations

- MathematicsSIAM J. Math. Anal.
- 2001

We establish that the Cauchy problem for the Benjamin--Ono equation and for a rather general class of nonlinear dispersive equations with dispersion slightly weaker than that of the Korteweg--de…

Well-posedness of the Cauchy problem for the modified KdV equation with periodic boundary condition

- Mathematics
- 2004

We study the time local well-posedness of the Cauchy problem for the modified KdV equation on the one-dimensional torus. We prove that when 1/2 > s > 3/8, it is locally well posed in H s , but the…