English

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

Analysis of PDEs 2018-05-17 v3

Abstract

We prove local in time well-posedness for a large class of quasilinear Hamiltonian, or parity preserving, Schr\"odinger 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.

Keywords

Cite

@article{arxiv.1711.02388,
  title  = {Local well-posedness for quasi-linear NLS with large Cauchy data on the circle},
  author = {Roberto Feola and Felice Iandoli},
  journal= {arXiv preprint arXiv:1711.02388},
  year   = {2018}
}

Comments

in press on "Annales de l'Institut Henri Poincar\'e C, Analyse Non Lin\'eaire"