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

Published 9 Mar 2015 in math.AP and math.DS | (1503.02468v2)

Abstract: 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 $Hs$ Sobolev norms. We also give estimates for the time required to attain this growth.

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