Global existence and uniqueness result for the diffusive Peterlin viscoelastic model. (June 2015)

• Record Type: Journal Article
• Authors: Lukáčová - Medvid'ová, Mária; Mizerová, Hana; Nečasová, Šárka
• Is Part Of: Nonlinear analysis. Volume 120(2015)
• Page Start: 154
• Page End: 170
• Publication Date: 2015-06
• Subjects: Peterlin viscoelastic model -- Existence -- Uniqueness; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2015.03.001
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: The aim of this paper is to present the existence and uniqueness result for the diffusive Peterlin viscoelastic model describing the unsteady behaviour of some incompressible polymeric fluids. The polymers are treated as two beads connected by a nonlinear spring. The Peterlin approximation of the spring force is used to derive the equation for the conformation tensor. The latter is the time evolution equation with spatial diffusion of the conformation tensor. Using the energy estimates we prove global in time existence of a weak solution in two space dimensions. We are also able to show the regularity and consequently the uniqueness of the weak solution.