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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
Abstract

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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Keywords
Klein–Gordon equation, Strichartz estimates, dispersive estimates
Mathematical Subject Classification
Primary: 37L50, 42B20
Milestones
Received: 23 August 2021
Revised: 12 May 2022
Accepted: 14 July 2022
Published: 21 January 2023
Authors
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