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

Emanuele Haus; Marcel Guardia; Michela Procesi

arxiv: 1503.02468 · v2 · pith:XCIUT5POnew · submitted 2015-03-09 · 🧮 math.AP · math.DS

Growth of Sobolev norms for the analytic NLS on mathbb T²

Marcel Guardia , Emanuele Haus , Michela Procesi This is my paper

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keywords growthanalyticequationnormssobolevachievearbitrarilyattain

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We consider the completely resonant defocusing non-linear Schr\"odinger equation on the two dimensional torus with any analytic gauge invariant nonlinearity. Fix $s>1$. We show the existence of solutions of this equation which achieve arbitrarily large growth of $H^s$ Sobolev norms. We also give estimates for the time required to attain this growth.

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Growth of Sobolev norms for the analytic NLS on mathbb T²

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