LOCAL WELL-POSEDNESS FOR THE QUASI-LINEAR HAMILTONIAN SCHRÖDINGER EQUATION ON TORI

Roberto Feola (1) , Felice Iandoli (2)

1 LMJL - Laboratoire de Mathématiques Jean Leray
2 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions

We prove a local in time well-posedness result for quasi-linear Hamiltonian Schrödinger equations on T d for any d ≥ 1. For any initial condition in the Sobolev space H s , with s large, we prove the existence and unicity 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.

Domaines: Mathématiques [math]; Equations aux dérivées partielles [math.AP]

Roberto Feola, Felice Iandoli. LOCAL WELL-POSEDNESS FOR THE QUASI-LINEAR HAMILTONIAN SCHRÖDINGER EQUATION ON TORI. 2020. ⟨hal-02504490v2⟩