Orateur
Rana Baddredine
(UCLA)
Description
The Benjamin-Ono equation is a canonical, completely integrable model for interface waves in stratified fluids of great depth. Recently, the orbital stability of its multisoliton solutions has been established in $H^s(\mathbb{R})$ for all $s > -1/2$. In this talk, we establish the asymptotic stability of these multisolitons under arbitrary, generic $L^2(\mathbb{R})$ perturbations, completely removing the need for spatial decay hypotheses. Relying on the explicit formula for the Benjamin-Ono flow, we evaluate the long-time limits of the solution along arbitrary spacetime rays to demonstrate that the flow ultimately decouples into individual solitons. This is joint work with Rowan Killip and Monica Vişan.