Analysis of a viscosity model for concentrated polymers

作者：Bulicek Miroslav^*; Gwiazda Piotr; Suli Endre; Swierczewska Gwiazda Agnieszka

来源：Mathematical Models and Methods in Applied Sciences, 2016, 26(8): 1599-1648.

DOI：10.1142/S0218202516500391

• Non-Newtonian fluid
• polymers
• monomers
• weak solution
• large-data existence

The paper is concerned with a class of mathematical models for polymeric fluids, which involves the coupling of the Navier-Stokes equations for a viscous, incompressible, constant-density fluid with a parabolic-hyperbolic integro-differential equation describing the evolution of the polymer distribution function in the solvent, and a parabolic integro-differential equation for the evolution of the monomer density function in the solvent. The viscosity coefficient, appearing in the balance of linear momentum equation in the Navier-Stokes system, includes dependence on the shear rate as well as on the weight-averaged polymer chain length. The system of partial differential equations under consideration captures the impact of polymerization and depolymerization effects on the viscosity of the fluid. We prove the existence of global-in-time, large-data weak solutions under fairly general hypotheses.

• 出版日期2016-7