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].
Local well-posedness for the quasi-linear Hamiltonian Schrödinger equation on tori
Feola R.;
2022-01-01
Abstract
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.File in questo prodotto:
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