Analysis & PDE

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

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

Emanuele Haus and Michela Procesi

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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
Received: 9 June 2014
Revised: 19 January 2015
Accepted: 6 March 2015
First available in Project Euclid: 16 November 2017

Permanent link to this document
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

Subjects
Primary: 35B34: Resonances 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10] 37K45: Stability problems

Keywords
nonlinear Schrödinger equation growth of Sobolev norms Hamiltonian PDEs weak turbulence

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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