We consider a two-dimensional nonlinear Schr"odinger equation with concentrated nonlinearity. In both the focusing and defocusing case we prove local well-posedness, i.e., existence and uniqueness of the solution for short times, as well as energy and mass conservation. In addition, we prove that this implies global existence in the defocusing case, irrespective of the power of the nonlinearity, while in the focusing case blowing-up solutions may arise.
Well-posedness of the two-dimensional nonlinear Schrödinger equation with concentrated nonlinearity
Correggi, Michele;
2019
Abstract
We consider a two-dimensional nonlinear Schr"odinger equation with concentrated nonlinearity. In both the focusing and defocusing case we prove local well-posedness, i.e., existence and uniqueness of the solution for short times, as well as energy and mass conservation. In addition, we prove that this implies global existence in the defocusing case, irrespective of the power of the nonlinearity, while in the focusing case blowing-up solutions may arise.File in questo prodotto:
| File | Dimensione | Formato | |
|---|---|---|---|
|
Well-posedness 2D NLS (CCT).pdf
Accesso chiuso
Tipologia:
Published version
Licenza:
Non pubblico
Dimensione
606.57 kB
Formato
Adobe PDF
|
606.57 kB | Adobe PDF | Richiedi una copia |
|
1702.03651.pdf
accesso aperto
Tipologia:
Submitted version (pre-print)
Licenza:
Creative Commons
Dimensione
442.9 kB
Formato
Adobe PDF
|
442.9 kB | Adobe PDF |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
