Orbital stability of the Benjamin-Ono equation in low-regularity spaces

We consider the Benjamin-Ono (BO) equation, a model for internal waves in deep stratified fluids. We prove the orbital stability of the multisolitons for the Benjamin-Ono equation in $H^s(\mathbb{R})$ for s>-\frac{1}{2}. Our proof relies on two key components: First, we establish a variational characterization of the multisolitons of (BO). And second, we develop a concentration-compactness principle adapted to the non-local structure of the equation. This is joint work with Rowan Killip and Monica Visan.