Existence of global weak solutions to the kinetic Hookean dumbbell model for incompressible dilute polymeric fluids. (February 2018)

• Record Type: Journal Article
• Authors: Barrett, John W.; Süli, Endre
• Is Part Of: Nonlinear analysis. Volume 39(2018)
• Page Start: 362
• Page End: 395
• Publication Date: 2018-02
• Subjects: Kinetic polymer models -- Hookean dumbbell model -- Navier–Stokes–Fokker–Planck system -- Dilute polymer -- Oldroyd-B model; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2017.07.012
• Languages: English
• ISSNs: 1468-1218

Abstract

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.