Luc Molinet
Published 2010-04-19, updated 2010-09-15Version 2
We prove that the solution-map $ u_0 \mapsto u $ associated with the KdV equation cannot be continuously extended in $ H^s(\R) $ for $ s<-1 $. The main ingredients are the well-known Kato smoothing effect for the mKdV equation as well as the Miura transform.
Comments: This preprint is an improved version of the previous preprint : "A remark on the ill-posedness issues for KdV and mKdV "
Airy and Painlevé asymptotics for the mKdV equation
Nonlinear Fourier transforms and the mKdV equation in the quarter plane
Ill-posedness of the incompressible Navier-Stokes equations in $\dot{F}^{-1,q}_{\infty}({R}^3)$
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