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
Download URL:
Submitted to ORA:
Submitted
Publication Type:
Journal Article