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Growth of Sobolev norms for abstract linear Schrödinger Equations

Alberto Maspero
Institution: 
SISSA
Location: 
A-005
Schedule: 
Friday, June 15, 2018 - 11:00
Abstract: 

We prove an abstract theorem giving a  $t^\epsilon$ bound for any $\epsilon> 0$ on the growth of the Sobolev norms in some abstract linear Schrödinger equations. The abstract theorem is applied to  nonresonant Harmonic oscillators in $R^d$. The proof is obtained by conjugating the system to some normal form in which the perturbation is a smoothing operator. Finally, time permitting, we will show how to construct a perturbation of the harmonic oscillator which provokes growth of Sobolev norms.

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