Nonlinear Partial Differential Equations

Date: March 8, 2022

Time: 3:00PM - 4:00PM

Location: Zoom

Speaker: Tristan Léger, Princeton University

Title: Long-time behavior of quadratic Klein-Gordon with internal mode in 3d

Abstract: In this talk I will present results on the small data regime of a quadratic Klein-Gordon equation with potential in 3d. This is motivated by the question of asymptotic stability of coherent structures in dispersive equations such as solitons.

The main novelty is the presence of an internal mode. We construct global solutions in this setting, and find that they have new features compared to the case with no internal mode. In particular they exhibit growth near certain frequencies, and have anomalously slow time decay. This is joint work with Fabio Pusateri.