What question did this study set out to answer?

The aim is to analyze how small molecular diffusivity and small noise intensity impact dissipation and decay in transport-diffusion processes.

April 17, 2026Open Access

Enhanced dissipation and Lyapunov exponents for stochastic transport-diffusion equations with small molecular diffusivity and small noise intensity

Key Points

The aim is to analyze how small molecular diffusivity and small noise intensity impact dissipation and decay in transport-diffusion processes.
Examined linear passive scalar transport-diffusion equations under white noise conditions.
Adapted and improved existing estimates for small diffusion and noise intensity regimes.
Aligned the study with Kolmogorov turbulence theory.
Identified enhanced dissipation rates under specified small-scale and low-intensity conditions.
Demonstrated improved decay properties in the modified model compared to previous work.

Abstract

Abstract The paper deals with linear passive scalar transport-diffusion equation subject to a velocity field which is white noise in time and is mainly active at small scales in space. The purpose is investigating the enhancement of dissipation and decay given by the small-scale transport. We modify and improve estimates from the previous work by Flandoli et al. (J. Differ. Equations 394 , 237–277, 2024), in order to investigate a different regime, namely small molecular diffusion and small noise intensity – corresponding to small turbulent kinetic energy. The noise specification is carefully tuned to Kolmogorov theory of turbulent fluids.

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