Scattering is shown for critical defocusing waves outside weakly trapping obstacles via infinite-time linear and nonlinear profile decompositions, assuming global Strichartz estimates, weak non-trapping, no reconcentration, and triviality of compact flows.
Ionescu, Benoit Pausader, and Gigliola Staffilani, On the global well-posedness of energy-critical S chr\"odinger equations in curved spaces , Anal
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On scattering and profile decomposition for critical nonlinear waves outside weakly trapping obstacles
Scattering is shown for critical defocusing waves outside weakly trapping obstacles via infinite-time linear and nonlinear profile decompositions, assuming global Strichartz estimates, weak non-trapping, no reconcentration, and triviality of compact flows.