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

Abstract

We consider the completely resonant defocusing non-linear Schrödinger 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.

References in corpus (3)

• A KAM algorithm for the resonant non--linear Schrödinger equation
• Resonant dynamics for the quintic non linear Schrödinger equation
• Energy cascades for NLS on the torus

Cited by in corpus (2)

• Turbulent cascades in a truncation of the cubic Szego equation and related systems
• Chaotic-like transfers of energy in Hamiltonian PDEs