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Unconditional uniqueness for the Benjamin–Ono equation

Răzvan Moşincat and Didier Pilod

Vol. 5 (2023), No. 2, 285–322
Abstract

We study the unconditional uniqueness of solutions to the Benjamin–Ono equation with initial data in Hs , 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.

Keywords
Benjamin–Ono equation, unconditional well-posedness, normal form method
Mathematical Subject Classification
Primary: 35A02, 35Q53
Secondary: 76B55
Milestones
Received: 25 October 2021
Revised: 26 September 2022
Accepted: 25 October 2022
Published: 26 June 2023
Authors
Răzvan Moşincat
Department of Mathematics
University of Bergen
Bergen
Norway
Department of Mathematics and Systems Engineering
Florida Institute of Technology
Melbourne, FL
United States
Didier Pilod
Department of Mathematics
University of Bergen
Bergen
Norway