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

Guàrdia Munarriz, Marcel; Sandhaus, Evan; Procesi, M.

doi:10.1016/j.aim.2016.06.018

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Guàrdia Munarriz, Marcel

Sandhaus, Evan

Procesi, M.

Document typeArticle

Defense date2016-10-01

Rights accessOpen Access

Except where otherwise noted, content on this work is licensed under a Creative Commons license : Attribution-NonCommercial-NoDerivs 3.0 Spain

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.

CitationGuardia, 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.

URIhttp://hdl.handle.net/2117/98644

DOI10.1016/j.aim.2016.06.018

ISSN0001-8708

Publisher versionhttp://www.sciencedirect.com/science/article/pii/S0001870816308015

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