Nonlinear Waves Trimester - June Conference

Collection Nonlinear Waves Trimester - June Conference

Organizer(s) T. Duyckaerts, F. Merle, J. Szeftel

Date(s) 20/06/2016 - 24/06/2016

linked URL https://indico.math.cnrs.fr/event/892/overview

00:00:00 / 00:00:00

5 23

Stability of Minkowski Space-time with a translation space-like Killing vector field

By Cécile Huneau

In the presence of a translation symmetry, the 3+1 vacuum Einstein equations reduce to the 2+1 Einstein equations with a scalar fi_eld. We work in generalised wave coordinates. In this gauge Einstein equations can be written as a system of quasilinear quadratic wave equations. The main diffi_culty in proving global existence of solutions for small data is due to the weaker decay of free solutions to the wave equation in 2+1 dimensions, compared to 3+1 dimensions. This weak decay seems to be a deterrent for proving a stability result in the usual wave coordinates. In this talk we will present the construction of a suitable generalized wave gauge in which our system has a "cubic weak null structure",which allows for the proof of global existence.

Information about the video

Date of recording 21/06/2016
Date of publication 04/07/2016
Institution IHES
Format MP4

Domain(s)

Analysis of PDEs

MSC codes

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