Global well-posedness for $H^{-1}(\mathbb{R})$ perturbations of KdV with exotic spatial asymptotics

Thierry Laurens

Given a suitable solution $V(t,x)$ to the Korteweg--de Vries equation on the real line, we prove global well-posedness for initial data $u(0,x)\in V(0,x)+H^{-1}(\mathbb{R})$. Ou…