Existence of global weak solutions to the kinetic Peterlin model

被引:6
作者
Gwiazda, P. [1 ,2 ]
Lukacova-Medvidova, M. [3 ]
Mizerova, H. [3 ,4 ,5 ]
Swierczewska-Gwiazda, A. [2 ]
机构
[1] Polish Acad Sci, Inst Math, Warsaw, Poland
[2] Univ Warsaw, Inst Appl Math & Mech, Warsaw, Poland
[3] Johannes Gutenberg Univ Mainz, Inst Math, Mainz, Germany
[4] Czech Acad Sci, Inst Math, Prague, Czech Republic
[5] Comenius Univ, Fac Math Phys & Informat, Bratislava, Slovakia
关键词
Kinetic theory; Dilute polymer solutions; Peterlin approximation; Navier-Stokes-Fokker-Planck system; Weak solution; SPRING CHAIN MODELS; DILUTE POLYMERS;
D O I
10.1016/j.nonrwa.2018.05.016
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
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 Suli (2018) we prove the existence of globalin-time weak solutions to the kinetic Peterlin model in two space dimensions. (C) 2018 Elsevier Ltd. All rights reserved.
引用
收藏
页码:465 / 478
页数:14
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