Abstract:
In this talk I will discuss some results about long time behaviors of solutions to Hamiltonian PDEs (Schrödinger, Kirchhoff, etc). In particular I will focus on a recent result where we (with J. Bernier, N. Camps and B. Grébert) prove exponential stability of small typical solutions of Schrödinger-Poisson equation by the so-called Rational Normal Form. For these resonant Hamiltonian PDEs the linear frequencies are fully resonant and we have to use the nonlinearity to avoid the resonances, which leads to a kind of new small divisors compared to Birkhoff Normal Form.
Il seminario avrà luogo presso il blocco aule del Dipartimento di Matematica e Fisica, Lungotevere Dante 376 - Aula M6
This post is also available in:
Link identifier #identifier__111944-5
Eng