Unconditional uniqueness for the Benjamin-Ono equation

Abstract

We study the unconditional uniqueness of solutions to the Benjamin-Ono equation with initial data in $H^s$, 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.

arXiv commentIn this new version the proof of the main estimate has been reorganized much more concisely following the referee suggestions. We have also justified the integrations by parts in the intermediate steps of the normal form transformations. To appear in Pure and Applied Analysis

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Cited by in corpus (3)

• Explicit formula for the Benjamin--Ono equation with square integrable and real valued initial data and applications to the zero dispersion limit
• Norm inflation for a higher-order nonlinear Schrödinger equation with a derivative on the circle
• Unconditional deep-water limit of the intermediate long wave equation in low-regularity