Global weak solutions to the Vlasov-Poisson-Fokker-Planck-Navier-Stokes system

TL;DR

This paper proves the global existence of weak solutions for a complex coupled system modeling charged particles in a fluid within a bounded domain, under certain conditions on the adiabatic coefficient.

Contribution

It establishes the first global weak solutions for the three-dimensional Vlasov-Poisson-Fokker-Planck-Navier-Stokes system with large data and nonhomogeneous boundary conditions.

Findings

Global weak solutions exist for $\gamma>3/2$

Solutions accommodate large initial and boundary data

The system models charged particles in a fluid in 3D bounded domains

Abstract

We consider the compressible Vlasov-Poisson-Fokker-Planck-Navier-Stokes system in a three dimensional bounded domain with nonhomogeneous Dirichlet boundary conditions. The system describes the evolution of charged particles ensemble dispersed in an isentropic fluid. For the adiabatic coefficient $\gamma>3/2$, we establish the global existence of weak solutions to this system with arbitrary large initial and boundary data.