Global weak solutions to the inhomogeneous Navier-Stokes-Vlasov equations

TL;DR

This paper proves the existence of global weak solutions for a coupled fluid-particle system described by inhomogeneous Navier-Stokes and Vlasov equations in three dimensions, addressing large initial data.

Contribution

It establishes the existence of global weak solutions for the inhomogeneous Navier-Stokes-Vlasov system in a bounded domain with large data, using approximation and energy methods.

Findings

Existence of global weak solutions proven

Applicable to large initial data

Method involves approximation and energy estimates

Abstract

A fluid-particle system of the inhomogeneous Navier-Stokes equations and Vlasov equation in the three dimensional space is considered in this paper. The coupling arises from the drag force in the fluid equations and the acceleration in the Vlasov equation. An initial-boundary value problem is studied in a bounded domain with large data. The existence of global weak solutions is established through an approximation scheme, energy estimates, and weak convergence.