ANALYSIS OF A DILUTE POLYMER MODEL WITH A TIME-FRACTIONAL DERIVATIVE

作     者：Fritz, Marvin Süli, Endre Wohlmuth, Barbara 

作者机构：Computational Methods for PDEs Johann Radon Institute for Computational and Applied Mathematics Altenberger Str. 69 Linz4040 Austria Mathematical Institute University of Oxford Andrew Wiles Building Woodstock Road OxfordOX2 6GG United Kingdom Department of Mathematics Technical University of Munich Boltzmannstr. 3 Garching bei München85748 Germany 

出 版 物：《arXiv》 (arXiv)

年 卷 期：2023年

核心收录：

主　　题：Fokker Planck equation 

摘      要：We investigate the well-posedness of a coupled Navier–Stokes–Fokker–Planck system with a time-fractional derivative. Such systems arise in the kinetic theory of dilute solutions of polymeric liquids, where the motion of noninteracting polymer chains in a Newtonian solvent is modelled by a stochastic process exhibiting power-law waiting time, in order to capture subdiffusive processes associated with non-Fickian diffusion. We outline the derivation of the model from a subordinated Langevin equation. The elastic properties of the polymer molecules immersed in the solvent are modelled by a finitely extensible nonlinear elastic (FENE) dumbbell model, and the drag term in the Fokker–Planck equation is assumed to be corotational. We prove the global-in-time existence of large-data weak solutions to this time-fractional model of order α ∈ (12 , 1), and derive an energy inequality satisfied by weak *** Codes 35Q30, 35Q84, 35R11, 60G22, 82C31, 82D60 © 2023, CC BY.