8 citations · 14 across the 4 of their papers we have counts for
4 papers
High-frequency solutions to the constraint equations
Arthur Touati
We construct high-frequency initial data for the Einstein vacuum equations in dimension 3+1 by solving the constraint equations on . Our family of solutions $(\bar{g}…
Geometric optics approximation for the Einstein vacuum equations
Arthur Touati
We show the stability of the geometric optics approximation in general relativity by constructing a family of high-frequency metrics solutions to the Einstein v…
Global existence of high-frequency solutions to a semi-linear wave equation with a null structure
Arthur Touati
We study the propagation of a compactly supported high-frequency wave through a semi-linear wave equation with a null structure. We prove that the self-interaction of the wave crea…
Einstein vacuum equations with symmetry in an elliptic gauge : local well-posedness and blow-up criterium
Arthur Touati
In this article, we are interested in the Einstein vacuum equations on a Lorentzian manifold displaying symmetry. We identify some freely prescribable initial data,…