Global Existence of classical solutions to 3D nonlinear Klein-Gordon equations with low-regularity initial data

Wei Xu; Yi Zhou

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arXiv · 2608.29250

Global Existence of classical solutions to 3D nonlinear Klein-Gordon equations with low-regularity initial data

Wei Xu·Yi Zhou

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Abstract

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.

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Wei Xu, Yi Zhou. 2026-08-29. Global Existence of classical solutions to 3D nonlinear Klein-Gordon equations with low-regularity initial data. https://arxiv.org/abs/2608.29250

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