# Kinetic Brownian motion on the diffeomorphism group of a closed Riemannian manifold

## TL;DR

This paper introduces kinetic Brownian motion on the diffeomorphism group of a closed Riemannian manifold, bridging fluid dynamics and stochastic flows with a novel mathematical framework.

## Contribution

It defines a new stochastic process on the diffeomorphism group that interpolates between hydrodynamic flow and Brownian motion.

## Key findings

- Establishes the mathematical foundation for kinetic Brownian motion on diffeomorphism groups.
- Shows the process interpolates between fluid flow and Brownian motion.
- Provides potential applications in fluid dynamics and stochastic analysis.

## Abstract

We define kinetic Brownian motion on the diffeomorphism group of a closed Riemannian manifold, and prove that it provides an interpolation between the hydrodynamic flow of a fluid and a Brownian-like flow.