19.3.2012
15:40
Prof. Endre Suli
(Mathematical Institute, University of Oxford):
Existence of global weak solutions to kinetic models of nonhomogeneous dilute polymeric fluids
Abstract: We prove the existence of global-in-time weak solutions to a general class of coupled bead-spring chain models that arise from the kinetic theory of dilute solutions of nonhomogeneous polymeric liquids with noninteracting polymer chains, with fi nitely extensible nonlinear elastic spring potentials. The class of models under consideration involves the unsteady incompressible Navier--Stokes equations with variable density and density-dependent dynamic viscosity in a bounded domain in two or three space dimensions for the density, the velocity and the pressure of the fluid, with an elastic extra-stress tensor appearing on the right-hand side in the momentum equation. The extra-stress tensor stems from the random movement of the polymer chains and is de fined by the Kramers expression through the associated probability density function that satisfi es a Fokker--Planck-type parabolic equation, a crucial feature of which is the presence of a centre-of-mass di ffusion term and a nonlinear density-dependent drag coefficient.


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