Existence of global weak solutions to compressible isentropic finitely extensible bead-spring chain models for dilute polymers

We prove the existence of global-in-time weak solutions to a general class of models that arise from the kinetic theory of dilute solutions of nonhomogeneous polymeric liquids, where the polymer molecules are idealized as bead-spring chains with finitely extensible nonlinear elastic (FENE) type spring potentials. The class of models under consideration involves the unsteady, compressible, isentropic, isothermal Navier-Stokes system in a bounded domain Omega in R-d, d = 2 or 3, for the density rho, the velocity (u) under tilde and the pressure p of the fluid, with an equation of state of the form p(rho) = c(p)rho gamma, where c(p) is a positive constant and gamma > 3/2. The right-hand side of the Navier-Stokes momentum equation includes an elastic extra-stress tensor, which is the sum of the classical Kramers expression and a quadratic interaction term. The elastic extra-stress tensor stems from the random movement of the polymer chains and is defined through the associated probability density function that satisfies a Fokker-Planck-type parabolic equation, a crucial feature of which is the presence of a center-of-mass diffusion term.