Local well-posedness for quasi-linear NLS with large Cauchy data on the circle
Annales de l'I.H.P. Analyse non linéaire, Tome 36 (2019) no. 1, pp. 119-164.

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.

DOI : 10.1016/j.anihpc.2018.04.003
Mots-clés : NLS, Quasi-linear PDEs, Para-differential calculus, Local wellposedness, Dispersive equations, Energy method 
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     author = {Feola, R. and Iandoli, F.},
     title = {Local well-posedness for quasi-linear {NLS} with large {Cauchy} data on the circle},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {119--164},
     publisher = {Elsevier},
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Feola, R.; Iandoli, F. Local well-posedness for quasi-linear NLS with large Cauchy data on the circle. Annales de l'I.H.P. Analyse non linéaire, Tome 36 (2019) no. 1, pp. 119-164. doi : 10.1016/j.anihpc.2018.04.003. https://www.numdam.org/articles/10.1016/j.anihpc.2018.04.003/

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