Dispersive dynamics of the Dirac equation on curved spaces and related problems

Federico Cacciafesta
Univ. Padova
Tuesday, May 22, 2018 - 14:30

The study of dispersive equations on non flat backgrounds is a problem that has attracted increasing interest in the last 20 years. The literature on the topic is huge and major breakthroughs have been achieved especially for the Schroedinger and wave equations. In this talk we intend to discuss dispersive properties for the Dirac equation in a non-flat setting, showing in particular how the Morawetz multiplier method can be adapted to prove local smoothing for asymptotically flat manifolds and how a “radial” decomposition of the operator (often referred to as “partial wave decomposition”) can be exploited to prove some weighted Strichartz estimates in the spherically symmetric case. 

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