# Pressureless Euler with nonlocal interactions as a singular limit of degenerate Navier-Stokes system

## TL;DR

This paper demonstrates that solutions of a degenerate Navier-Stokes system converge to solutions of a pressureless Euler system with additional forces, using the relative entropy method in one dimension.

## Contribution

It establishes a rigorous singular limit from degenerate Navier-Stokes equations to pressureless Euler equations with nonlocal interactions.

## Key findings

- Weak solutions of Navier-Stokes converge to Euler solutions
- Convergence proven using relative entropy method
- Results apply to systems with linear drag, Newtonian repulsion, and quadratic confinement

## Abstract

We show that weak solutions of degenerate Navier-Stokes equations converge to the strong solutions of the pressureless Euler system with linear drag term, Newtonian repulsion and quadratic confinement. The proof is based on the relative entropy method using the artificial velocity formulation for the one-dimensional Navier-Stokes system.