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Unconditional uniqueness
for the Benjamin–Ono equation
Răzvan Moşincat and Didier Pilod |
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Vol. 5 (2023), No. 2, 285–322
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Abstract |
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We study the unconditional uniqueness of solutions to the Benjamin–Ono equation with initial data in , 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 . As a by-product of our proof, we also obtain a nonlinear smoothing property on the gauge variable at the same level of regularity. |
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Keywords
Benjamin–Ono equation, unconditional well-posedness, normal
form method
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Mathematical Subject Classification
Primary: 35A02, 35Q53
Secondary: 76B55
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Milestones
Received: 25 October 2021
Revised: 26 September 2022
Accepted: 25 October 2022
Published: 26 June 2023
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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 |
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| © 2023 MSP (Mathematical Sciences Publishers). |
