# On Dean-Kawasaki Dynamics with Smooth Drift Potential

## TL;DR

This paper investigates the Dean-Kawasaki equation with smooth drift potential, establishing conditions under which measure-valued solutions exist and linking them to finite Langevin particle systems with mean field interactions.

## Contribution

It demonstrates the existence of measure-valued solutions only in specific parameter regimes and connects these solutions to finite Langevin particle systems with mean field interactions.

## Key findings

- Measure-valued solutions exist only in certain parameter regimes.
- Solutions correspond to finite Langevin particle systems with mean field interaction.
- Provides conditions for existence of solutions in the Dean-Kawasaki equation.

## Abstract

We consider the Dean-Kawasaki equation with smooth drift interaction potential and show that measure valued solutions exist only in certain parameter regimes in which case they are given by finite Langevin particle systems with mean field interaction.