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About the wave equation outside two strictly convex obstacles

Abstract We prove global Strichartz estimates without loss for the wave equation outside two strictly convex obstacles, following the road-map previously introduced by the author for the Schrödinger equation. Moreover, we show a first step towards the large data scattering for the critical non-linear equation associated to this geometrical setting, and prove the scattering for a class of non-trapping obstacles close to the two convex framework.