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

Oana Ivanovici

doi:10.3934/dcds.2021093

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2021, Volume 41, Issue 12: 5707-5742. Doi: 10.3934/dcds.2021093 open access

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

Oana Ivanovici

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

Received: December 31, 2020

Revised: March 31, 2021

Early access: June 2021

Published: December 2021

The author is supported by ERC grant ANADEL 757 996

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Abstract

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.

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Mathematics Subject Classification: Primary: 35Rxx; Secondary: 58Jxx.

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