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Bibliographic Details
Main Authors: Li, Xue-Mei, Sobczak, Szymon
Format: Preprint
Published: 2026
Subjects:
Online Access:https://arxiv.org/abs/2601.21762
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author Li, Xue-Mei
Sobczak, Szymon
author_facet Li, Xue-Mei
Sobczak, Szymon
contents We define a bona fide rough path solution for the Navier-Stokes equation with an additional rough transport term, and show that the SPDE on the three-dimensional torus driven by a fractional Brownian motion on $H^σ$ has solutions characterised as the effective limits of a slow/fast system. We further show that this rough path solution is equivalent to the widely used incremental notion of solution (the unbounded rough driver formulation), demonstrating broader applicability to other nonlinear SPDEs.
format Preprint
id arxiv_https___arxiv_org_abs_2601_21762
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Navier-Stokes with a fractional transport noise as a limit of multi-scale dynamics
Li, Xue-Mei
Sobczak, Szymon
Probability
Analysis of PDEs
We define a bona fide rough path solution for the Navier-Stokes equation with an additional rough transport term, and show that the SPDE on the three-dimensional torus driven by a fractional Brownian motion on $H^σ$ has solutions characterised as the effective limits of a slow/fast system. We further show that this rough path solution is equivalent to the widely used incremental notion of solution (the unbounded rough driver formulation), demonstrating broader applicability to other nonlinear SPDEs.
title Navier-Stokes with a fractional transport noise as a limit of multi-scale dynamics
topic Probability
Analysis of PDEs
url https://arxiv.org/abs/2601.21762