%0 Journal Article %J Mathematics in Engineering %D 2022 %T Long-time stability of the quantum hydrodynamic system on irrational tori %A Roberto Feola %A Felice Iandoli %A Federico Murgante %K Euler-Korteweg %K irrational tori %K long time stability %K QHD system %K Small divisors %B Mathematics in Engineering %V 4 %P 1-24 %G eng %U https://www.aimspress.com/article/doi/10.3934/mine.2022023 %R 10.3934/mine.2022023 %0 Journal Article %J Annales de l'Institut Henri Poincaré C, Analyse non linéaire %D 2019 %T Local well-posedness for quasi-linear NLS with large Cauchy data on the circle %A Roberto Feola %A Felice Iandoli %K Dispersive equations %K Energy method %K Local wellposedness %K NLS %K Para-differential calculus %K Quasi-linear PDEs %X

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.

%B Annales de l'Institut Henri Poincaré C, Analyse non linéaire %V 36 %P 119 - 164 %G eng %U http://www.sciencedirect.com/science/article/pii/S0294144918300428 %R https://doi.org/10.1016/j.anihpc.2018.04.003