## Analysis & PDE

• Anal. PDE
• Volume 8, Number 4 (2015), 883-922.

### Growth of Sobolev norms for the quintic NLS on $T^2$

#### 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.

#### Article information

Source
Anal. PDE, Volume 8, Number 4 (2015), 883-922.

Dates
Revised: 19 January 2015
Accepted: 6 March 2015
First available in Project Euclid: 16 November 2017

https://projecteuclid.org/euclid.apde/1510843116

Digital Object Identifier
doi:10.2140/apde.2015.8.883

Mathematical Reviews number (MathSciNet)
MR3366006

Zentralblatt MATH identifier
1322.35126

#### Citation

Haus, Emanuele; Procesi, Michela. Growth of Sobolev norms for the quintic NLS on $T^2$. Anal. PDE 8 (2015), no. 4, 883--922. doi:10.2140/apde.2015.8.883. https://projecteuclid.org/euclid.apde/1510843116

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