Abstract
We prove that the solution-map $ u_0 \mapsto u $ associated with the KdV equation cannot be continuously extended in $ H^s(\mathbb R) $ for $ s<-1 $. The main ingredients are the well-known Kato smoothing effect for the mKdV equation as well as the Miura transform.
Citation
Luc Molinet. "A note on ill posedness for the KdV equation." Differential Integral Equations 24 (7/8) 759 - 765, July/August 2011. https://doi.org/10.57262/die/1356628831
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