29 jan 2020 -- 09:30 [open in google calendar]
Scuola Normale Superiore, Aula Bianchi Scienze
We present some recent results on the twodimensional nonlinear Schrödinger equation with concentrated nonlinearity. We start by discussing local well-posedness of the associated Cauchy problem, as well as mass and energy conservation along the flow. Then, we show that in the repulsive case solutions are global-in-time, whereas in the attractive case one can exhibit a class of initial data that gives rise to blow-up phenomena. Finally, we present the family of the standing waves of the problem, and discuss their stability properties.
These are joint works with R. Adami, R. Carlone, M. Correggi and A. Fiorenza.