Global wellposedness of KdV in H−1(T,R)

Abstract

By the inverse method we show that the Korteweg–de Vries equation (KdV) ∂tv(x,t)=-∂x3v(x,t)+6v(x,t)∂xv(x,t) (x∈T,t∈R) is globally (in time) wellposed in the Sobolev space of distributions Hβ(T,R) for any β≥−1