The Pressureless Euler-Navier-Stokes System

In this paper, we study the well-posedness of the pressureless Euler-Navier-Stokes system in ${\mathbb{R}}^d$ (with $d\ge 2$) 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.