In this note, we discuss the nonlinear stability in exponential time of Minkowki space-time with a translation space-like Killing field, proved in [13]. In the presence of such a symmetry, the vacuum Einstein equations reduce to the Einstein equations with a scalar field. We work in generalized wave coordinates. In this gauge Einstein equations can be written as a system of quasilinear quadratic wave equations. The main difficulty in [13] is due to the decay in of free solutions to the wave equation in dimensions, which is weaker than in dimensions. As in [21], we have to rely on the particular structure of Einstein equations in wave coordinates. We also have to carefully chose an approximate solution with a non trivial behaviour at space-like infinity to enforce convergence to Minkowski space-time at time-like infinity. This article appears under the same form in the proceedings of the Laurent Schwartz seminar.
@incollection{JEDP_2015____A3_0,
author = {C\'ecile Huneau},
title = {Stability in exponential time of {Minkowski} space-time with a space-like translation symmetry},
booktitle = {},
series = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
eid = {3},
pages = {1--12},
publisher = {Groupement de recherche 2434 du CNRS},
year = {2015},
doi = {10.5802/jedp.632},
language = {en},
url = {https://proceedings.centre-mersenne.org/articles/10.5802/jedp.632/}
}
TY - JOUR AU - Cécile Huneau TI - Stability in exponential time of Minkowski space-time with a space-like translation symmetry JO - Journées équations aux dérivées partielles PY - 2015 SP - 1 EP - 12 PB - Groupement de recherche 2434 du CNRS UR - https://proceedings.centre-mersenne.org/articles/10.5802/jedp.632/ DO - 10.5802/jedp.632 LA - en ID - JEDP_2015____A3_0 ER -
%0 Journal Article %A Cécile Huneau %T Stability in exponential time of Minkowski space-time with a space-like translation symmetry %J Journées équations aux dérivées partielles %D 2015 %P 1-12 %I Groupement de recherche 2434 du CNRS %U https://proceedings.centre-mersenne.org/articles/10.5802/jedp.632/ %R 10.5802/jedp.632 %G en %F JEDP_2015____A3_0
Cécile Huneau. Stability in exponential time of Minkowski space-time with a space-like translation symmetry. Journées équations aux dérivées partielles (2015), article no. 3, 12 p. doi : 10.5802/jedp.632. https://proceedings.centre-mersenne.org/articles/10.5802/jedp.632/
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