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On the absence of blow-up in the 3D Navier-Stokes equations with transport noise
Abstract
Establishing the global-in-time smoothness of solutions to the 3D Navier-Stokes equations (NSEs) with large initial data remains a long-standing open problem. In this paper, we prove that the 3D NSEs driven by a suitably chosen transport noise -- a physically motivated stochastic perturbation -- admit global-in-time smooth solutions with high probability. This regularizing effect holds uniformly for initial data in arbitrarily large balls of subcritical function spaces with positive smoothness.
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BibTeX
@misc{agresti2026absence,
title = {{On the absence of blow-up in the 3D Navier-Stokes equations with transport noise}},
author = {Antonio Agresti},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.15140},
eprint = {2607.15140},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.15140},
}
RIS
TY - UNPB
TI - On the absence of blow-up in the 3D Navier-Stokes equations with transport noise
AU - Antonio Agresti
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2607.15140
UR - https://arxiv.org/abs/2607.15140
AB - Establishing the global-in-time smoothness of solutions to the 3D Navier-Stokes equations (NSEs) with large initial data remains a long-standing open problem. In this paper, we prove that the 3D NSEs driven by a suitably chosen transport noise -- a physically motivated stochastic perturbation -- admit global-in-time smooth solutions with high probability. This regularizing effect holds uniformly for initial data in arbitrarily large balls of subcritical function spaces with positive smoothness.
ER -