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Growth of Sobolev norms in the cubic defocusing nonlinear Schrödinger equation

Autor
Guardia, M.; Kaloshin, V.
Tipus d'activitat
Article en revista
Revista
Journal of the European Mathematical Society
Data de publicació
2015
Volum
17
Número
1
Pàgina inicial
71
Pàgina final
149
DOI
https://doi.org/10.4171/JEMS/499 Obrir en finestra nova
Repositori
http://hdl.handle.net/2117/114593 Obrir en finestra nova
URL
http://www.ems-ph.org/journals/show_abstract.php?issn=1435-9855&vol=17&iss=1&rank=3 Obrir en finestra nova
Resum
We consider the cubic defocusing nonlinear Schrödinger equation in the two dimensional torus. Fix s>1. Recently Colliander, Keel, Staffilani, Tao and Takaoka proved the existence of solutions with s -Sobolev norm growing in time. We establish the existence of solutions with polynomial time estimates. More exactly, there is c>0 such that for any K»1 we find a solution u and a time T such that ¿u(T)¿Hs=K¿u(0)¿Hs. Moreover, the time T satisfies the polynomial bound 0
Citació
Guardia, M., Kaloshin, V. Growth of Sobolev norms in the cubic defocusing nonlinear Schrödinger equation. "Journal of the European Mathematical Society", 2015, vol. 17, núm. 1, p. 71-149.
Grup de recerca
SD - Sistemes Dinàmics de la UPC

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