标题： 半克莱因-戈登方程在渐近平坦背景上的斯特里哈特估计及其对三次狄拉克方程的应用 显示英文标题

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

摘要： 本文的目的是在弱渐近平坦时空上建立(半) Klein-Gordon 方程的$L^2_t$-端点 Strichartz 估计。 作为应用，我们证明了在此设定下质量三次狄拉克方程在完整次临界范围内的小数据全局适定性和散射。 关键的组成部分是按照 Metcalfe-Tataru 和 Xue 的工作进行的参数构造，并补充了 Zheng-Zhang 获得的 Strichartz 估计。 三次狄拉克方程全局结果的证明遵循 Machihara-Nakanishi-Ozawa 在欧几里得设定中开发的策略。 显示英文摘要

摘要： 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.