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arXiv · 2611.03519

Stability of negative-regularity mixing and applications to stochastic fluids

Antonio Agresti·William Cooperman·Patrick Flynn
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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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Antonio Agresti, William Cooperman, Patrick Flynn. 2026-11-02. Stability of negative-regularity mixing and applications to stochastic fluids. https://arxiv.org/abs/2611.03519

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