Sharp ill-posedness and well-posedness results for the KdV-Burgers equation: the periodic case

Luc Molinet, Stéphane Vento

We prove that the KdV-Burgers is globally well-posed in $ H^{-1}(\T) $ with a solution-map that is analytic from $H^{-1}(\T) $ to $C([0,T];H^{-1}(\T))$ whereas it is ill-posed in $…