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Growth of Sobolev norms for abstract linear Schrödinger Equations

  • Date November 9, 2017
  • Hour 3 pm
  • Room GSSI Main Lecture Hall
  • Speaker Alberto Maspero (SISSA)

ABSTRACT

We prove an abstract theorem giving a epsilon bound for any  t^\epsilon bound for any \epsilon> 0 on the growth of the Sobolev norms in some abstract linear time dependent Schrödinger equations.
The abstract theorem is applied to several cases, including perturbations of (i) Schrödinger equation on a Zoll manifold; (ii) resonant or 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. This is a joint work with D. Bambusi, B. Grebert and D. Robert.