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Growth of Sobolev norms for the analytic NLS on T-2

Author
Guardia, M.; Sandhaus, E.; Procesi, M.
Type of activity
Journal article
Journal
Advances in mathematics
Date of publication
2016-10-01
Volume
301
First page
615
Last page
692
DOI
https://doi.org/10.1016/j.aim.2016.06.018 Open in new window
Repository
http://hdl.handle.net/2117/98644 Open in new window
https://arxiv.org/abs/1503.02468 Open in new window
URL
http://www.sciencedirect.com/science/article/pii/S0001870816308015 Open in new window
Abstract
We consider the completely resonant non-linear Schrödinger equation on the two dimensional torus with any analytic gauge invariant nonlinearity. Fix s>1. We show the existence of solutions of this equation which achieve arbitrarily large growth of Hs Sobolev norms. We also give estimates for the time required to attain this growth.
Citation
Guardia, M., Sandhaus, E., Procesi, M. Growth of Sobolev norms for the analytic NLS on T-2. "Advances in mathematics", 1 Octubre 2016, vol. 301, p. 615-692.
Keywords
Growth of Sobolev norms, Hamiltonian partial differential equations, Nonlinear Schrodinger equation, Transfer of energy
Group of research
SD - UPC Dynamical Systems

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