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Delayed blow-up by transport noise for the 3D Navier-Stokes equation with Navier-slip boundary conditions
[Submitted on 17 Jun 2026] · 2026-06-18 · via math.PR updates on arXiv.org

Mathematics > Analysis of PDEs

arXiv:2606.19060 (math)

[Submitted on 17 Jun 2026]

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Abstract:We study the vorticity formulation of the 3D Navier-Stokes equation driven by transport noise in a periodic channel with Navier-slip boundary conditions. We consider both non-degenerate transport noise and degenerate tangential transport noise. For any prescribed $T>0$ and $\epsilon>0$, we prove that, by choosing the noise intensity sufficiently large and concentrating the noise on sufficiently high modes, the solution exists up to $T$ with probability at least $1-\epsilon$.
A main contribution of this work is to identify and analyze the interaction between enhanced dissipation induced by transport noise and physical boundary effects. The no-flux condition breaks the isotropy of the noise and changes the scaling limit of the Itô-Stratonovich corrector. In the non-degenerate case, a boundary feedback term appears in the limiting effective operator; in the degenerate case, the limiting operator is a nonlocal anisotropic tangential dissipation. The proof is based on a combination of a boundary correction operator, a Meyers-type estimate, a scaling-limit analysis of the Itô-Stratonovich corrector, and resolvent estimates for the deterministic limiting equations.

Submission history

From: Meng Zhao [view email]
[v1] Wed, 17 Jun 2026 13:30:33 UTC (54 KB)

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