The Pressureless Euler-Navier-Stokes System

TL;DR

This paper establishes global existence and decay estimates for the pressureless Euler-Navier-Stokes system in critical regularity for small initial data in multiple dimensions.

Contribution

It provides the first well-posedness and decay results for the pressureless Euler-Navier-Stokes system in critical regularity.

Findings

Global existence for small initial data

Optimal decay rates in time

Well-posedness in critical regularity setting

Abstract

In this paper, we study the well-posedness of the pressureless Euler-Navier-Stokes system in $\mathbb{R}^d$ (with $d\geq 2$) in the critical regularity setting for a density close to $0$. We prove a global existence result for small data for this system, and then give optimal time decay estimates.