Local well-posedness for quasi-linear NLS with large Cauchy data on the circle

Abstract

We prove local in time well-posedness for a large class of quasilinear Hamiltonian, or parity preserving, Schrödinger equations on the circle. After a paralinearization of the equation, we perform several paradifferential changes of coordinates in order to transform the system into a paradifferential one with symbols which, at the positive order, are constant and purely imaginary. This allows to obtain a priori energy estimates on the Sobolev norms of the solutions.

in press on "Annales de l'Institut Henri Poincaré C, Analyse Non Linéaire"

References in corpus (2)

• KAM for autonomous quasi-linear perturbations of mKdV
• Gravity capillary standing water waves

Cited by in corpus (4)

• Reducibility of Schrödinger equation on a Zoll manifold with unbounded potential
• Long time existence for fully nonlinear NLS with small Cauchy data on the circle
• Long time solutions for quasi-linear Hamiltonian perturbations of Schrödinger and Klein-Gordon equations on tori
• Local well-posedness for the quasi-linear Hamiltonian Schrödinger equation on tori