Global weak solutions to a quantum kinetic-fluid model with large initial data

Abstract

In this paper, we consider a quantum kinetic-fluid model in one-dimensional torus. This model consists of the Vlasov–Fokker–Planck equation coupled with the compressible quantum Navier–Stokes equations via a nonlinear friction force depends on the density of the fluid. The quantum fluid with degenerate viscosity is assumed to be isentropic (adiabatic coefficient γ>1). We establish the global weak solutions to this model with arbitrary large initial data. This is the first result on existence of solutions to kinetic-fluid models with density-dependent friction force and degenerate viscosity.