University of Cambridge > Talks.cam > Geometric Analysis and Partial Differential Equations seminar > Stability in exponential time of Minkowski Space-time with a translation space-like Killing field

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

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  • UserCecile Huneau, ENS
  • ClockMonday 11 May 2015, 15:00-16:00
  • HouseCMS, MR13.

If you have a question about this talk, please contact Amit Einav.

In the presence of a translation space-like Killing field the 3 1 vacuum Einstein equations reduce to the 2 1 Einstein equations with a scalar field. We work in generalised wave coordinates. In this gauge Einstein equations can be written as a system of quasilinear quadratic wave equations. The main difficulty is due to the weak decay of free solutions to the wave equation in 2 dimensions. To prove long time existence of solutions, we have to rely on the particular structure of Einstein equations in wave coordinates. We also have to carefully choose the behaviour of our metric in the exterior region to enforce convergence to Minkowski space-time at time-like infinity.

This talk is part of the Geometric Analysis and Partial Differential Equations seminar series.

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