Appears in collection : Day in Honor of Yvonne Choquet-Bruhat’s 100 th Birthday

In this talk, I will present two works of Yvonne Choquet-Bruhat. The first one, written in 1969, concerns the behaviour of high-frequency gravitationnal waves, and enlighten the beautiful structure of Einstein equations. She has subsequently generalized this work to Einstein equations coupled with other fields (electromagnetic, fluid...). The second more recent work I will speek about concerns the global existence of cosmological solutions with U(1) symmetry, with the introduction of the elliptic gauge. I will then present a work in collaboration with Jonathan Luk, about high-frequency solutions of Einstein equations with U(1) symmetry, in which the elliptic gauge is a very nice setting to study the superposition of waves.