具有低正则性初值的三维非线性克莱因-戈登方程经典解的整体存在性
Global Existence of classical solutions to 3D nonlinear Klein-Gordon equations with low-regularity initial data
- Nanchang Hangkong University（南昌航空大学）
- Fudan University（复旦大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文针对三维非线性克莱因-戈登方程柯西问题，在经典局部存在性的正则性范围内，借助Georgiev与Popivanov的相关结果及新建立的Klainerman-Sobolev型不等式，通过高低阶能量估计证明其经典解的整体存在性。
AI中文摘要：
本文严格在经典局部存在性的正则性范围内，研究三维非线性克莱因-戈登方程柯西问题的整体存在性，通过高阶与低阶能量估计完成证明。证明依赖两个关键要素：其一源自Georgiev与Popivanov的工作，将二次非线性项约化为三次项加幽灵能量可控项，以确保低阶估计；其二是本文建立的不含缩放算子的尖锐Klainerman-Sobolev型不等式，该不等式为二阶导数提供足够时间衰减，分部积分可控制高阶估计中的导数损失项。
英文摘要：
This paper studies global existence for the Cauchy problem of nonlinear Klein-Gordon equations in three space dimensions, strictly within the regularity regime of classical local existence. We prove it via higher-order and lower-order energy estimates. The proof relies on two key ingredients. The first is due to the work of Georgiev and Popivanov, which reduces quadratic nonlinearities to cubic terms plus ghost-energy-controllable terms, securing lower-order estimates. The second is a sharp Klainerman-Sobolev-type inequality without the scaling operator, established herein, which yields enough time decay for derivatives up to second order; integration by parts then controls derivative loss terms in the higher-order estimates.
