# Lagrangian coordinates for the sticky particle system

## TL;DR

This paper demonstrates the existence of solutions for the one-dimensional sticky particle system using Lagrangian coordinates, contributing to the mathematical understanding of particle interactions in cosmological structure formation.

## Contribution

It introduces a method to construct solutions for the sticky particle system in one dimension via Lagrangian trajectory mappings, advancing the theoretical framework.

## Key findings

- Existence of solutions in one dimension established
- Trajectory mapping in Lagrangian coordinates constructed
- Applicable to Zel'dovich's theory of large-scale structure formation

## Abstract

The sticky particle system is a system of partial differential equations which assert the conservation of mass and momentum of a collection of particles that interact only via inelastic collisions. These equations arise in Zel'dovich's theory for the formation of large scale structures in the universe. We will show that this system of equations has a solution in one spatial dimension for given initial conditions by generating a trajectory mapping in Lagrangian coordinates.