# Density of Inertial Particles: Exactly Solvable 2D Models

## TL;DR

This paper derives exact bounds for the mean number of caustics in 2D inertial particles under Gaussian noise, providing insights into particle clustering behavior with verified numerical accuracy.

## Contribution

It introduces exactly solvable 2D models for inertial particles and establishes bounds on caustic formation, advancing understanding of particle dynamics in stochastic flows.

## Key findings

- Bounds for caustic numbers are established for different forcing types.
- Numerical methods confirm the efficiency of the derived bounds.
- The models enhance understanding of inertial particle behavior in stochastic environments.

## Abstract

Inertial particles in 2D driven by a Gaussian white noise forcing are considered. For two examples of the forcing (compressible and incompressible) upper and lower bounds are found for the mean number of caustics as a function of Stokes number. Efficiency of the bounds is verified by numerical methods.