@article {FEOLA2019119, title = {Local well-posedness for quasi-linear NLS with large Cauchy data on the circle}, journal = {Annales de l{\textquoteright}Institut Henri Poincar{\'e} C, Analyse non lin{\'e}aire}, volume = {36}, number = {1}, year = {2019}, pages = {119 - 164}, abstract = {

We prove local in time well-posedness for a large class of quasilinear Hamiltonian, or parity preserving, Schr{\"o}dinger 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 = {Dispersive equations, Energy method, Local wellposedness, NLS, Para-differential calculus, Quasi-linear PDEs}, issn = {0294-1449}, doi = {https://doi.org/10.1016/j.anihpc.2018.04.003}, url = {http://www.sciencedirect.com/science/article/pii/S0294144918300428}, author = {Roberto Feola and Felice Iandoli} }