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arXiv · 2507.11422

A Stochastic RAGE Theorem and Enhanced Dissipation for Transport Noise

Michele Coti Zelati·Martin Hairer·David Villringer
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Abstract

We prove a stochastic version of the classical RAGE theorem that applies to the two-point motion generated by noisy transport equations. As a consequence, we identify a necessary and sufficient condition for the corresponding diffusive equation to be dissipation enhancing. This involves the identification of a non-trivial, finite dimensional subspace that is invariant for the family of self-adjoint operator characterizing the structure of the transport noise. We discuss several examples and prove a sharp enhanced dissipation rate for stochastic shear flows.

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Michele Coti Zelati, Martin Hairer, David Villringer. 2025-07-15. A Stochastic RAGE Theorem and Enhanced Dissipation for Transport Noise. https://arxiv.org/abs/2507.11422

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