Dia: Dimecres, 4 d'octubre de 2023
Lloc: Aula S04, Facultat de Matemàtiques i Estadística, UPC. Pau Gargallo,14 BCN.
A càrrec de: Filippo Giuliani (Politecnico de Milano)
Títol: Sobolev instability for the cubic NLS on irrational tori.
Resum: In the last two decades the study of instability in Sobolev spaces for nonlinear Hamiltonian partial differential equations on compact manifolds has drawn lots of attention in the mathematical community. A breaktrough result in this sense is due to Colliander-Keel-Staffilani-Takaoka-Tao (Invent. Math 2010), who showed the existence of solutions to the defocusing cubic NLS on the 2-dimensional square torus with arbitrarily small initial data and arbitrarily large Sobolev norms at later times. The mechanism to construct such unstable solutions is based on the study of the resonant dynamics of NLS and it has inspired several other works. However, Staffilani noticed that the same strategy would not applied for the NLS equation on 2-dimensional irrational tori, where the resonant structure is less rich.In this talk we discuss how we overcame this problem to prove Sobolev instability for the cubic NLS on irrational tori. Moroever, we present a recent result of this type where we take into account also the presence of smooth convolution potentials.
Last updated: Sat Sep 30 10:52:48 2023