Existence of global weak solutions to the kinetic Peterlin model

0490609 - MÚ 2019 RIV GB eng J - Článek v odborném periodiku
Gwiazda, P. - Lukáčová-Medviďová, M. - Mizerová, Hana - Świerczewska, A.
Existence of global weak solutions to the kinetic Peterlin model.
Nonlinear Analysis: Real World Applications. Roč. 44, December (2018), s. 465-478. ISSN 1468-1218. E-ISSN 1878-5719
Grant CEP: GA ČR(CZ) GA18-05974S
Institucionální podpora: RVO:67985840
Klíčová slova: dilute polymer solutions * kinetic theory * Navier–Stokes–Fokker–Planck system * Peterlin approximation
Obor OECD: Pure mathematics
Impakt faktor: 2.085, rok: 2018
https://www.sciencedirect.com/science/article/pii/S1468121818305480

We consider a class of kinetic models for polymeric fluids motivated by the Peterlin dumbbell theories for dilute polymer solutions with a nonlinear spring law for an infinitely extensible spring. The polymer molecules are suspended in an incompressible viscous Newtonian fluid confined to a bounded domain in two or three space dimensions. The unsteady motion of the solvent is described by the incompressible Navier–Stokes equations with the elastic extra stress tensor appearing as a forcing term in the momentum equation. The elastic stress tensor is defined by Kramer's expression through the probability density function that satisfies the corresponding Fokker–Planck equation. In this case a coefficient depending on the average length of polymer molecules appears in the latter equation. Following the recent work of Barrett and Süli (2018) we prove the existence of global-in-time weak solutions to the kinetic Peterlin model in two space dimensions.
Trvalý link: http://hdl.handle.net/11104/0284781