Knocking out teeth in one-dimensional periodic NLS
Chaichenets, Leonid
; Hundertmark, Dirk; Kunstmann, Peer; Pattakos, Nikolaos
; Hundertmark, Dirk; Kunstmann, Peer; Pattakos, NikolaosAbstract:
We show the existence of weak solutions in the extended sense of the Cauchy problem for the cubic nonlinear Schrödinger equation in one dimension with initial data u0 in H$^{s1}$(R)+H$^{s2}$(T),0≤s1≤s2. In addition, we show that if u0∈H$^{s}$(R)+H$^{1/2ϵ}$(T) where ϵ>0 and 1/6≤s≤1/2 the solution is unique in H$^{s}$(R)+H$^{1/2ϵ}$(T). Our main tool is a normal form type reduction via the use of the differentiation by parts technique.
| Zugehörige Institution(en) am KIT | Institut für Analysis (IANA) Sonderforschungsbereich 1173 (SFB 1173) |
| Publikationstyp | Forschungsbericht/Preprint |
| Publikationsjahr | 2018 |
| Sprache | Englisch |
| Identifikator | ISSN: 2365-662X urn:nbn:de:swb:90-868846 KITopen-ID: 1000086884 |
| Verlag | Karlsruher Institut für Technologie (KIT) |
| Umfang | 38 S. |
| Serie | CRC 1173 ; 2018/20 |
| Schlagwörter | normal form method, nonlinear Schrodinger, local wellposedness, Sobolev spaces |