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arXiv · 1702.06502

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

John W. Barrett·Endre Süli
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Abstract

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

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John W. Barrett, Endre Süli. 2017-02-21. Existence of global weak solutions to the kinetic Hookean dumbbell model for incompressible dilute polymeric fluids. https://arxiv.org/abs/1702.06502

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