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

Emanuele Haus; Michela Procesi

arxiv: 1405.1538 · v1 · pith:NURECMTTnew · submitted 2014-05-07 · 🧮 math.AP

Growth of Sobolev norms for the quintic NLS on mathbb T²

Emanuele Haus , Michela Procesi This is my paper

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keywords normsquinticsobolevaccurateanalysiscasecombinatorialcubic

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We study the quintic Non Linear Schr\"odinger 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.

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Growth of Sobolev norms for the quintic NLS on mathbb T²

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