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We explore the existence of global weak solutions to the Hookean dumbbellmodel, a system of nonlinear partial differential equations that arises fromthe kinetic theory of dilute polymers, involving the unsteady incompressibleNavier--Stokes equations in a bounded domain in two or three space dimensions,coupled to a Fokker--Planck-type parabolic equation. We prove the existence oflarge-data global weak solutions in the case of two space dimensions.Indirectly, our proof also rigorously demonstrates that, in two spacedimensions at least, the Oldroyd-B model is the macroscopic closure of theHookean dumbbell model. In three space dimensions, we prove the existence oflarge-data global weak subsolutions to the model, which are weak solutions witha defect measure, where the defect measure appearing in the Navier--Stokesmomentum equation is the divergence of a symmetric positive semidefinitematrix-valued Radon measure.

Existence of global weak solutions to the kinetic Hookean dumbbell model for incompressible dilute polymeric fluids