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Stability of negative-regularity mixing and applications to stochastic fluids
Abstract
We consider mixing for a scalar advected by random vector fields, such as solutions to stochastic fluid equations. Our main abstract result is that contraction in expectation of a negative Sobolev norm of the scalar (negative-regularity mixing) is stable under perturbations of the joint scalar-velocity process. We apply the result in three settings: mixing for a hyperviscous Boussinesq-type system where the scalar actively drives the velocity, mixing for a passive scalar advected by two-dimensional Navier-Stokes driven by smooth-in-time stochastic forcing, and a black-box proof that negative-regularity mixing implies enhanced dissipation.
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BibTeX
@misc{agresti2026stability,
title = {{Stability of negative-regularity mixing and applications to stochastic fluids}},
author = {Antonio Agresti and William Cooperman and Patrick Flynn},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.03519},
eprint = {2611.03519},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.03519},
}
RIS
TY - UNPB
TI - Stability of negative-regularity mixing and applications to stochastic fluids
AU - Antonio Agresti
AU - William Cooperman
AU - Patrick Flynn
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.03519
UR - https://arxiv.org/abs/2611.03519
AB - We consider mixing for a scalar advected by random vector fields, such as solutions to stochastic fluid equations. Our main abstract result is that contraction in expectation of a negative Sobolev norm of the scalar (negative-regularity mixing) is stable under perturbations of the joint scalar-velocity process. We apply the result in three settings: mixing for a hyperviscous Boussinesq-type system where the scalar actively drives the velocity, mixing for a passive scalar advected by two-dimensional Navier-Stokes driven by smooth-in-time stochastic forcing, and a black-box proof that negative-regularity mixing implies enhanced dissipation.
ER -