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2015 Growth of Sobolev norms for the quintic NLS on $T^2$
Emanuele Haus, Michela Procesi
Anal. PDE 8(4): 883-922 (2015). DOI: 10.2140/apde.2015.8.883

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.

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Emanuele Haus. Michela Procesi. "Growth of Sobolev norms for the quintic NLS on $T^2$." Anal. PDE 8 (4) 883 - 922, 2015. https://doi.org/10.2140/apde.2015.8.883

Information

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

zbMATH: 1322.35126
MathSciNet: MR3366006
Digital Object Identifier: 10.2140/apde.2015.8.883

Subjects:
Primary: 35B34 , 35Q55 , 37K45

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

Rights: Copyright © 2015 Mathematical Sciences Publishers

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