Global stability for nonlinear wave equations with multi-localized initial data

Global stability for nonlinear wave equations with multi-localized initial data

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Federico Pasqualotto, Princeton University
Fine Hall 314

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. 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. We finally use a modified version of the classical Klainerman-Sobolev inequality, which takes into account the special structure of the data. This is joint work with John Anderson (Princeton University).