Carlos E. Kenig, Gustavo Ponce, Luis Vega
Published 2019-01-31Version 1
We prove that if $u_1,\,u_2$ are solutions of the Benjamin-Ono equation defined in $ (x,t)\in\R \times [0,T]$ which agree in an open set $\Omega\subset \R \times [0,T]$, then $u_1\equiv u_2$. We extend this uniqueness result to a general class of equations of Benjamin-Ono type in both the initial value problem and the initial periodic boundary value problem. This class of 1-dimensional non-local models includes the intermediate long wave equation. Finally, we present a slightly stronger version of our uniqueness results for the Benjamin-Ono equation.
Unconditional deep-water limit of the intermediate long wave equation in low-regularity
On the integrability of the Benjamin-Ono equation on the torus
Stability in $H^{1/2}$ of the sum of $K$ solitons for the Benjamin-Ono equation
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