Strichartz estimates for the half Klein-Gordon equation on asymptotically flat backgrounds and applications to cubic Dirac equations

Sebastian Herr; Seokchang Hong

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arXiv · 2502.13670

Strichartz estimates for the half Klein-Gordon equation on asymptotically flat backgrounds and applications to cubic Dirac equations

Sebastian Herr·Seokchang Hong

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Abstract

The aim of this paper is to establish the $L^2_t$-endpoint Strichartz estimate for (half) Klein-Gordon equations on a weakly asymptotically flat space-time. As an application we prove small data global well-posedness and scattering for massive cubic Dirac equations in the full subcritical range in this setting. Crucial ingredient is a parametrix contruction following the work of Metcalfe-Tataru and Xue and complements Strichartz estimates obtained by Zheng-Zhang. The proof of the global result for the cubic Dirac equation follows the strategy developed by Machihara-Nakanishi-Ozawa in the Euclidean setting.

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Sebastian Herr, Seokchang Hong. 2025-02-19. Strichartz estimates for the half Klein-Gordon equation on asymptotically flat backgrounds and applications to cubic Dirac equations. https://arxiv.org/abs/2502.13670

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