Enhanced Dissipation via the Malliavin Calculus

TL;DR

This paper uses Malliavin Calculus to analyze enhanced dissipation phenomena, providing a simplified proof of known timescales and regularization effects in shear flows.

Contribution

It introduces an elementary approach to establish enhanced dissipation timescales and hypoelliptic regularization, simplifying previous complex proofs.

Findings

Reproduces the enhanced dissipation timescale for shear flows.

Demonstrates precise hypoelliptic regularization in the x-direction.

Provides a concise, elementary proof technique.

Abstract

In this work we investigate the phenomenon of enhanced dissipation using techniques from the Malliavin Calculus. In particular, we construct a concise, elementary argument, that allows us to recover the well-known enhanced dissipation timescale for shear flows, first obtained by Bedrossian and Coti Zelati in 2017, as well as the precise hypoelliptic regularisation in x.