Arthur Touati

most citedHigh-frequency solutions to the constraint equations

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math.AP2021

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…

math.AP2021

Einstein vacuum equations with $U (1)$ 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 $U (1)$ symmetry. We identify some freely prescribable initial data,…

Global existence of high-frequency solutions to a semi-linear wave equation with a null structure

Einstein vacuum equations with U(1) symmetry in an elliptic gauge : local well-posedness and blow-up criterium

Einstein vacuum equations with $U (1)$ symmetry in an elliptic gauge : local well-posedness and blow-up criterium