  We consider a class of kinetic models for polymeric fluids motivated by the
Peterlin dumbbell theories for dilute polymer solutions with a nonlinear spring
law for an infinitely extensible spring. The polymer molecules are suspended in
an incompressible viscous Newtonian fluid confined to a bounded domain in two
or three space dimensions. The unsteady motion of the solvent is described by
the incompressible Navier-Stokes equations with the elastic extra stress tensor
appearing as a forcing term in the momentum equation. The elastic stress tensor
is defined by the Kramers expression through the probability density function
that satisfies the corresponding Fokker-Planck equation. In this case, a
coefficient depending on the average length of polymer molecules appears in the
latter equation. Following the recent work of Barrett and S\"uli we prove the
existence of global-in-time weak solutions to the kinetic Peterlin model in two
space dimensions.
