Growth of Sobolev norms for the quintic NLS on ${\mathbb{T}}^2$

Abstract

We study the quintic Non Linear 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 used in the case of the cubic NLS. This requires an accurate combinatorial analysis.

41 pages, 5 figures. arXiv admin note: text overlap with arXiv:0808.1742 by other authors

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