Seminario di Analisi Matematica

Mercoledì 10 maggio 2023, alle ore 14:30, Stefano Pasquali (Université Paris-Saclay) terrà un Seminario di Analisi Matematica, dal titolo "An energy cascade phenomenon for a Klein-Gordon lattice"

Abstract:

In this talk I will present a result about the dynamics of a d-dimensional Klein-Gordon lattice with periodic boundary conditions, for d ≤ 3. 
If we consider initial data supported on one low-frequency Fourier mode, we can show that, in the continuous approximation, the resonant normal form of the system is given by a small-dispersion nonlinear Schrödinger (NLS) equation. 
Exploiting a result by Kuksin about the growth of Sobolev norms for the small-dispersion NLS, we describe an energy cascade phenomenon for the Klein-Gordon lattice, where part of the energy is transferred to modes associated to higher frequencies. 
Such a phenomenon holds within the time-scale for which we can ensure the validity of the continuous approximation.

Il seminario avrà luogo presso il Dipartimento di Matematica e Fisica, L.go S. L. Murialdo 1 - Aula 211