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.
De Patrick Gerard
De Hatem Zaag
De Thomas Kappeler
De Michal Kowalczyk
De Cécile Huneau
De Mihalis Dafermos
De Andrea Nahmod
De Benjamin Schlein
De Chris Sogge
De Alexandru Ionescu
De Vlad Vicol
De Thomas Alazard
De Robert Jerrard
De Camillo de Lellis
De Albert Schwarz
De Chao Li
De Albert Schwarz
De Albert Schwarz
De Stephen Coombes , Peter Liddle
De Victor Kleptsyn
De Albert Schwarz
