English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We reformulate a general class of classical bead-spring-chain models fordilute polymeric fluids, with Hookean spring potentials, as McKean-Vlasovdiffusion. This results in a coupled system of partial differential equationsinvolving the unsteady incompressible linearized Navier-Stokes equations,referred to as the Oseen system, for the velocity and the pressure of thefluid, with a source term which is a nonlinear function of the probabilitydensity function, and a second-order degenerate parabolic Fokker-Planckequation, whose transport terms depend on the velocity field, for theprobability density function. We show that this coupled Oseen-Fokker-Plancksystem has a large-data global weak solution. We then perform a rigorouspassage to the limit as the masses of the beads in the bead-spring-chainconverge to zero, which is shown in particular to result in equilibration inmomentum space. The limiting problem is then used to perform a rigorousderivation of the Hookean bead-spring-chain model for dilute polymeric fluids,which has the interesting feature that, if the flow domain is bounded, then sois the associated configuration space domain and the associated Kramers stresstensor is defined by integration over this bounded configuration domain.

McKean-Vlasov diffusion and the well-posedness of the Hookean  bead-spring-chain model for dilute polymeric fluids: small-mass limit and  equilibration in momentum space