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 Ω in Rd, d = 2 or 3, for the density ρ, the velocity u∼
and the pressure p of
the fluid, with an equation of state of the form p(ρ) = cpρ
γ, where cp is a positive constant
and γ > 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 centre-of-mass diffusion term.