Vol. 8, No. 4, 2015

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

Emanuele Haus and Michela Procesi

Vol. 8 (2015), No. 4, 883–922

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.

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