#### 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
##### 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