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December  2021, 41(12): 5707-5742. doi: 10.3934/dcds.2021093

## Dispersive estimates for the wave and the Klein-Gordon equations in large time inside the Friedlander domain

 Sorbonne Université, CNRS, LJLL, F-75005 Paris, France

Received  January 2021 Revised  April 2021 Published  December 2021 Early access  June 2021

Fund Project: The author is supported by ERC grant ANADEL 757 996

We prove global in time dispersion for the wave and the Klein-Gordon equation inside the Friedlander domain by taking full advantage of the space-time localization of caustics and a precise estimate of the number of waves that may cross at a given, large time. Moreover, we uncover a significant difference between Klein-Gordon and the wave equation in the low frequency, large time regime, where Klein-Gordon exhibits a worse decay than the wave, unlike in the flat space.

Citation: Oana Ivanovici. Dispersive estimates for the wave and the Klein-Gordon equations in large time inside the Friedlander domain. Discrete & Continuous Dynamical Systems, 2021, 41 (12) : 5707-5742. doi: 10.3934/dcds.2021093
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