Global weak solutions to the Navier-Stokes-Vlasov equations

TL;DR

This paper proves the existence of global weak solutions for the coupled Navier-Stokes-Vlasov system in three dimensions and establishes uniqueness in two dimensions, advancing understanding of particle-fluid interactions.

Contribution

It demonstrates the existence of global weak solutions in 3D and uniqueness in 2D for the Navier-Stokes-Vlasov equations, a novel result in coupled particle-fluid models.

Findings

Global weak solutions exist in three dimensions.

Unique global solutions are established in two dimensions.

The coupled system models particle-fluid interactions effectively.

Abstract

In this paper, the system of particles coupled with fluid is considered. The particles are described by a Vlasov equation, and the fluid is governed by a forced Navier-Stokes equations. The interaction with fluid phase governed by Navier-Stokes equations is taken into account through a source term. The resulting system, namely Navier-Stokes-Vlasov equations, is shown to have global weak solutions in three spatial dimensions, and to have a unique global solution in two spatial dimensions.