analysis of partial differential equations

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

arXiv:2502.13670

summary

The paper establishes endpoint Strichartz estimates for half Klein‑Gordon equations on weakly asymptotically flat spacetimes and uses them to prove small‑data global well‑posedness and scattering for massive cubic Dirac equations in the full subcritical range.

Abstract

The aim of this paper is to establish the -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.

v1: 42pages. v2: 41 pages, major revision and corrections. v3: 43 pages, major revision and further corrections

Topics & keywords

#strichartz estimates#klein-gordon equation#dirac equation#asymptotically flat spacetimes#global well-posednessL^2_t endpointparametrix constructionweakly asymptotically flatcubic nonlinearitymassive Diracsubcritical range
Strichartz estimates for the half Klein-Gordon equation on asymptotically flat backgrounds and applications to cubic Dirac equations · wovepaper