Existence of global weak solutions to compressible isentropic finitely extensible bead-spring chain models for dilute polymers
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 spri...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
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World Scientific Publishing
2015
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| _version_ | 1826287196014903296 |
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| author | Barrett, JW Süli, E |
| author_facet | Barrett, JW Süli, E |
| author_sort | Barrett, JW |
| collection | OXFORD |
| description | 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 Ω in Rd, d=2 or 3, for the density ρ, the velocity u˜ and the pressure p of the fluid, with an equation of state of the form p(ρ)=cpργ, where cp is a positive constant and γ>32. 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. |
| first_indexed | 2024-03-07T01:55:00Z |
| format | Journal article |
| id | oxford-uuid:9b6a1cb4-aecb-4ce7-b840-4ac95c9e65c7 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T01:55:00Z |
| publishDate | 2015 |
| publisher | World Scientific Publishing |
| record_format | dspace |
| spelling | oxford-uuid:9b6a1cb4-aecb-4ce7-b840-4ac95c9e65c72022-03-27T00:28:36ZExistence of global weak solutions to compressible isentropic finitely extensible bead-spring chain models for dilute polymersJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:9b6a1cb4-aecb-4ce7-b840-4ac95c9e65c7EnglishSymplectic Elements at OxfordWorld Scientific Publishing2015Barrett, JWSüli, EWe 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 Ω in Rd, d=2 or 3, for the density ρ, the velocity u˜ and the pressure p of the fluid, with an equation of state of the form p(ρ)=cpργ, where cp is a positive constant and γ>32. 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. |
| spellingShingle | Barrett, JW Süli, E Existence of global weak solutions to compressible isentropic finitely extensible bead-spring chain models for dilute polymers |
| title | Existence of global weak solutions to compressible isentropic finitely extensible bead-spring chain models for dilute polymers |
| title_full | Existence of global weak solutions to compressible isentropic finitely extensible bead-spring chain models for dilute polymers |
| title_fullStr | Existence of global weak solutions to compressible isentropic finitely extensible bead-spring chain models for dilute polymers |
| title_full_unstemmed | Existence of global weak solutions to compressible isentropic finitely extensible bead-spring chain models for dilute polymers |
| title_short | Existence of global weak solutions to compressible isentropic finitely extensible bead-spring chain models for dilute polymers |
| title_sort | existence of global weak solutions to compressible isentropic finitely extensible bead spring chain models for dilute polymers |
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