The APDE seminar on Monday, 10/05, will be given by Federico Pasqualotto online via Zoom from 4:10 to 5pm. To participate, email Georgios Moschidis (firstname.lastname@example.org) or Federico Pasqualotto (email@example.com).
Title: Global stability for nonlinear wave equations with multi-localized initial data.
Abstract: The classical global existence theory for nonlinear wave equations requires initial data to be small and localized around a point. In this work, we initiate the study of the global stability of nonlinear wave equations with non localized data.
In particular, we extend the classical theory to data localized around several points. This is achieved by generalizing the vector field method to the multi-localized case.
The core of our argument lies in a close inspection of the geometry of two interacting waves emanating from different localized sources. We show trilinear estimates to control such interaction, by means of a physical space method. This is joint work with John Anderson (Princeton University).