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 HsSobolev norms. We also give estimates for the time required to attain this growth.

Guardia, M., Haus, E., Procesi, M. (2016). Growth of Sobolev norms for the analytic NLS on T2. ADVANCES IN MATHEMATICS, 301, 615-692 [10.1016/j.aim.2016.06.018].

Growth of Sobolev norms for the analytic NLS on T2

Haus, Emanuele;Procesi, M.
2016-01-01

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 HsSobolev norms. We also give estimates for the time required to attain this growth.
2016
Guardia, M., Haus, E., Procesi, M. (2016). Growth of Sobolev norms for the analytic NLS on T2. ADVANCES IN MATHEMATICS, 301, 615-692 [10.1016/j.aim.2016.06.018].
File in questo prodotto:
File Dimensione Formato  
GHPNLSRevision.pdf

accesso aperto

Descrizione: articolo principale
Tipologia: Documento in Post-print
Dimensione 691.4 kB
Formato Adobe PDF
691.4 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11590/327681
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 33
  • ???jsp.display-item.citation.isi??? 31
social impact