| Title | Local well-posedness for quasi-linear NLS with large Cauchy data on the circle |
| Publication Type | Journal Article |
| Year of Publication | 2019 |
| Authors | Feola, R, Iandoli, F |
| Journal | Annales de l'Institut Henri Poincaré C, Analyse non linéaire |
| Volume | 36 |
| Pagination | 119 - 164 |
| ISSN | 0294-1449 |
| Keywords | Dispersive equations; Energy method; Local wellposedness; NLS; Para-differential calculus; Quasi-linear PDEs |
| 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. |
| URL | http://www.sciencedirect.com/science/article/pii/S0294144918300428 |
| DOI | 10.1016/j.anihpc.2018.04.003 |
Research Group: