We prove a local in time well-posedness result for quasi-linear Hamiltonian Schrödinger equations on Td for any d≥1. For any initial condition in the Sobolev space Hs, with s large, we prove the existence and uniqueness of classical solutions of the Cauchy problem associated to the equation. The lifespan of such a solution depends only on the size of the initial datum. Moreover we prove the continuity of the solution map.
Feola, R., & Iandoli, F. (2022). Local well-posedness for the quasi-linear Hamiltonian Schrödinger equation on tori. JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES, 157, 243-281 [10.1016/j.matpur.2021.11.009].
Titolo: | Local well-posedness for the quasi-linear Hamiltonian Schrödinger equation on tori | |
Autori: | ||
Data di pubblicazione: | 2022 | |
Rivista: | ||
Citazione: | Feola, R., & Iandoli, F. (2022). Local well-posedness for the quasi-linear Hamiltonian Schrödinger equation on tori. JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES, 157, 243-281 [10.1016/j.matpur.2021.11.009]. | |
Handle: | http://hdl.handle.net/11590/396992 | |
Appare nelle tipologie: | 1.1 Articolo in rivista |