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

Author: 

Barrett, J
Süli, E

Publication Date: 

10 August 2017

Journal: 

Nonlinear Analysis Series B: Real World Applications

Last Updated: 

2019-04-27T18:57:26.327+01:00

Issue: 

February 2018

Volume: 

Volume 36,

DOI: 

10.1016/j.nonrwa.2017.07.012

page: 

362-395

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.

Symplectic id: 

684031

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Submitted to ORA: 

Submitted

Publication Type: 

Journal Article