PreprintarXiv licencearXiv
Global Existence of classical solutions to 3D nonlinear Klein-Gordon equations with low-regularity initial data
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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BibTeX
@misc{xu2026global,
title = {{Global Existence of classical solutions to 3D nonlinear Klein-Gordon equations with low-regularity initial data}},
author = {Wei Xu and Yi Zhou},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.29250},
eprint = {2608.29250},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.29250},
}
RIS
TY - UNPB
TI - Global Existence of classical solutions to 3D nonlinear Klein-Gordon equations with low-regularity initial data
AU - Wei Xu
AU - Yi Zhou
PY - 2026
DA - 2026/08/29
PB - arXiv
DO - 10.48550/arxiv.2608.29250
UR - https://arxiv.org/abs/2608.29250
AB - 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.
ER -