PreprintarXiv licencearXiv
Non-time-decaying global classical solutions to nonlinear wave equations in 3D under the null condition
Abstract
We present an alternative proof of the global well-posedness of nonlinear wave equations in three spatial dimensions under the null condition, in the regularity regime of the classical local existence theory, assuming smallness of the angular derivatives. Unlike previous methods, which rely on decay in time, our approach is based solely on spatial decay. This provides a new perspective on the problem and offers potential applications to the study of Einstein's equations, which we intend to explore in future work.
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BibTeX
@misc{zhang2026nontimedecaying,
title = {{Non-time-decaying global classical solutions to nonlinear wave equations in 3D under the null condition}},
author = {Zexian Zhang and Yi Zhou},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.29500},
eprint = {2608.29500},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.29500},
}
RIS
TY - UNPB
TI - Non-time-decaying global classical solutions to nonlinear wave equations in 3D under the null condition
AU - Zexian Zhang
AU - Yi Zhou
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2608.29500
UR - https://arxiv.org/abs/2608.29500
AB - We present an alternative proof of the global well-posedness of nonlinear wave equations in three spatial dimensions under the null condition, in the regularity regime of the classical local existence theory, assuming smallness of the angular derivatives. Unlike previous methods, which rely on decay in time, our approach is based solely on spatial decay. This provides a new perspective on the problem and offers potential applications to the study of Einstein's equations, which we intend to explore in future work.
ER -