On the absence of blow-up in the 3D Navier-Stokes equations with transport noise

Antonio Agresti

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arXiv · 2607.15140

On the absence of blow-up in the 3D Navier-Stokes equations with transport noise

Antonio Agresti

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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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Antonio Agresti. 2026-07-16. On the absence of blow-up in the 3D Navier-Stokes equations with transport noise. https://arxiv.org/abs/2607.15140

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