학술논문
Existence of global weak solutions to compressible isentropic finitely extensible bead-spring chain models for dilute polymers.
Document Type
Article
Author
Source
Subject
*EXISTENCE theorems
*COMPRESSIBLE flow
*ISENTROPIC processes
*DILUTION
*POLYMER solutions
*NAVIER-Stokes equations
*NONLINEAR theories
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Language
ISSN
0218-2025
Abstract
We prove the existence of global-in-time weak solutions to a general class of models that arise from the kinetic theory of dilute solutions of nonhomogeneous polymeric liquids, where the polymer molecules are idealized as bead-spring chains with finitely extensible nonlinear elastic (FENE) type spring potentials. The class of models under consideration involves the unsteady, compressible, isentropic, isothermal Navier-Stokes system in a bounded domain in , or , for the density , the velocity and the pressure of the fluid, with an equation of state of the form , where is a positive constant and . The right-hand side of the Navier-Stokes momentum equation includes an elastic extra-stress tensor, which is the sum of the classical Kramers expression and a quadratic interaction term. The elastic extra-stress tensor stems from the random movement of the polymer chains and is defined through the associated probability density function that satisfies a Fokker-Planck-type parabolic equation, a crucial feature of which is the presence of a center-of-mass diffusion term. [ABSTRACT FROM AUTHOR]