Sharp ill-posedness and well-posedness results for the KdV-Burgers equation: the real line case
We complete the known results on the local Cauchy problem in Sobolev spaces for the KdV-Burgers equation by proving that this equation is well-posed in $ H^{-1}(\R) $ with a solution-map that is analytic from $H^{-1}(\R) $ to $C([0,T];H^{-1}(\R))$ whereas it is ill-posed in $ H^s(\R) $, as soon as $...
Gespeichert in:
| Veröffentlicht in: | Annali della Scuola normale superiore di Pisa, Classe di scienze Classe di scienze, 2011-01, Vol.10 (3), p.531-560 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Zusammenfassung: | We complete the known results on the local Cauchy problem in Sobolev spaces for the KdV-Burgers equation by proving that this equation is well-posed in $ H^{-1}(\R) $ with a solution-map that is analytic from $H^{-1}(\R) $ to $C([0,T];H^{-1}(\R))$ whereas it is ill-posed in $ H^s(\R) $, as soon as $ s |
|---|---|
| ISSN: | 0391-173X 2036-2145 |
| DOI: | 10.2422/2036-2145.2011.3.02 |