Growth of Sobolev norms for the analytic NLS on $\mathbb T^2$
Analysis of PDEs
2017-06-16 v2 Dynamical Systems
Abstract
We consider the completely resonant defocusing non-linear Schr\"odinger equation on the two dimensional torus with any analytic gauge invariant nonlinearity. Fix . We show the existence of solutions of this equation which achieve arbitrarily large growth of Sobolev norms. We also give estimates for the time required to attain this growth.
Keywords
Cite
@article{arxiv.1503.02468,
title = {Growth of Sobolev norms for the analytic NLS on $\mathbb T^2$},
author = {Marcel Guardia and Emanuele Haus and Michela Procesi},
journal= {arXiv preprint arXiv:1503.02468},
year = {2017}
}