Vol. 8, No. 4, 2015

Download this article
Download this article For screen
For printing
Recent Issues

Volume 10
Issue 7, 1539–1791
Issue 6, 1285–1538
Issue 5, 1017–1284
Issue 4, 757–1015
Issue 3, 513–756
Issue 2, 253–512
Issue 1, 1–252

Volume 9, 8 issues

Volume 8, 8 issues

Volume 7, 8 issues

Volume 6, 8 issues

Volume 5, 5 issues

Volume 4, 5 issues

Volume 3, 4 issues

Volume 2, 3 issues

Volume 1, 3 issues

The Journal
Cover
About the Cover
Editorial Board
Editors’ Interests
About the Journal
Scientific Advantages
Submission Guidelines
Submission Form
Subscriptions
Editorial Login
Contacts
Author Index
To Appear
 
ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
Growth of Sobolev norms for the quintic NLS on $T^2$

Emanuele Haus and Michela Procesi

Vol. 8 (2015), No. 4, 883–922
Abstract

We study the quintic nonlinear Schrödinger equation on a two-dimensional torus and exhibit orbits whose Sobolev norms grow with time. The main point is to reduce to a sufficiently simple toy model, similar in many ways to the one discussed by Colliander et al. for the case of the cubic NLS. This requires an accurate combinatorial analysis.

Keywords
nonlinear Schrödinger equation, growth of Sobolev norms, Hamiltonian PDEs, weak turbulence
Mathematical Subject Classification 2010
Primary: 35B34, 35Q55, 37K45
Milestones
Received: 9 June 2014
Revised: 19 January 2015
Accepted: 6 March 2015
Published: 21 June 2015
Authors
Emanuele Haus
Dipartimento di Matematica e Applicazioni “R. Caccioppoli”
Università di Napoli “Federico II”
Via Cintia, Monte S. Angelo
I-80126 Napoli
Italy
Michela Procesi
Dipartimento di Matematica
Università di Roma “La Sapienza”
Piazzale Aldo Moro, 5
I-00185 Roma
Italy