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Strichartz estimates for the Klein–Gordon equation in $\mathbb{R}^{3+1}$

Marius Beceanu and Gong Chen

Vol. 4 (2022), No. 4, 767–809

We prove standard and reversed Strichartz estimates for the Klein–Gordon equation in 3+1 . Instead of the Fourier theory, our analysis is based on fundamental solutions of the free equations and fractional integrations. We apply Strichartz estimates to study semilinear Klein–Gordon equations.

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Klein–Gordon equation, Strichartz estimates, dispersive estimates
Mathematical Subject Classification
Primary: 37L50, 42B20
Received: 23 August 2021
Revised: 12 May 2022
Accepted: 14 July 2022
Published: 21 January 2023
Marius Beceanu
Department of Mathematics and Statistics
University at Albany SUNY
Albany, NY
United States
Gong Chen
School of Mathematics
Georgia Institute of Technology
Atlanta, GA
United States