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En utilisant une méthode dépendante du temps, nous démontrons la complétude asymptotique
pour l'équation des ondes dans une classe d'espaces-temps stationnaires et
asymptotiquement plats. On introduit l'observable de vitesse asymptotique et on décrit
son spectre (sous des hypothèses plus faibles que pour la complétude asymptotique). Les
méthodes utilisées sont inspirées par celles de l'analyse du problème à deux corps en
mécanique quantique.
In this paper we consider a smooth and bounded domain of dimension with boundary and we construct sequences of solutions to the wave equation with Dirichlet boundary condition which contradict the Strichartz estimates of the free space, providing losses of derivatives at least for a subset of the usual range of indices. This is due to microlocal phenomena such as caustics generated in arbitrarily small time near the boundary. Moreover, the result holds for microlocally strictly convex domains...
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