A note on ill posedness for the KdV equation
By Luc Molinet. Differential and Integral Equations, 2010
54 citations recorded by the source corpus.
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.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/cf369c703f374914be00124a360ce2ae4d429357
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
- Rowan Killip
- Monica Visan
- Luc Molinet
- Barry Simon
- B. Dodson
- Benoit Pausader
- Didier Pilod
- Vedran Sohinger
In Mathematical Physics
- Rowan Killip
- Monica Visan
- Luc Molinet
- B. Dodson
- Carlos E. Kenig
- Aynur Bulut
- Vedran Sohinger
- F. Merle
Citations in the corpus
- KdV is well-posed in H–1 (2018, background): “The papers [51, 52] show that well-posedness cannot persist (in either geometry) in H for any s < −1.”
- Lower Bounds on the Radius of Spatial Analyticity for the KdV Equation (2015, unknown): “It is by now known that local well-posedness holds in H for s ≥ −3/4 (see [4,14]) and that for s < −3/4, there is ill-posedness (see [4,15,18]).”
- Sharp ill-posedness results for the KdV and mKdV equations on the torus (2011, methodology): “Finally, we follow some ideas of [17] and use properties of the Riccati map proved in [10] to derive a non continuity result for the KdV equation in Hs(T) for s < −1.”