Global weak solutions for a Vlasov–Fokker–Planck/Navier–Stokes system with nonhomogeneous boundary data

Abstract

In this paper, we consider a kinetic-fluid model with nonhomogeneous Dirichlet boundary data in a 3D bounded domain. This model consists of a Vlasov–Fokker–Planck equation coupled with the compressible Navier–Stokes equations via a friction force. We establish the global existence of weak solutions to it for the isentropic fluid (adiabatic coefficient $$\gamma > \frac{3}{2}$$ ) with large initial data, and large velocity and density at the inflow boundary.