Existence of global weak solutions to the kinetic Peterlin model. (December 2018)

• Record Type: Journal Article
• Authors: Gwiazda, P.; Lukáčová-Medvidová, M.; Mizerová, H.; Świerczewska-Gwiazda, A.
• Is Part Of: Nonlinear analysis. Volume 44(2018)
• Page Start: 465
• Page End: 478
• Publication Date: 2018-12
• Subjects: Kinetic theory -- Dilute polymer solutions -- Peterlin approximation -- Navier–Stokes–Fokker–Planck system -- Weak solution; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2018.05.016
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: We consider a class of kinetic models for polymeric fluids motivated by the Peterlin dumbbell theories for dilute polymer solutions with a nonlinear spring law for an infinitely extensible spring. The polymer molecules are suspended in an incompressible viscous Newtonian fluid confined to a bounded domain in two or three space dimensions. The unsteady motion of the solvent is described by the incompressible Navier–Stokes equations with the elastic extra stress tensor appearing as a forcing term in the momentum equation. The elastic stress tensor is defined by Kramer's expression through the probability density function that satisfies the corresponding Fokker–Planck equation. In this case a coefficient depending on the average length of polymer molecules appears in the latter equation. Following the recent work of Barrett and Süli (2018) we prove the existence of global-in-time weak solutions to the kinetic Peterlin model in two space dimensions.