Analysis of a dilute polymer model with a time-fractional derivative

[2307.16606] Analysis of a dilute polymer model with a time-fractional derivative Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Analysis of PDEs arXiv:2307.16606 (math) [Submitted on 31 Jul 2023] Title: Analysis of a dilute polymer model with a time-fractional derivative Authors: Marvin Fritz , Endre Süli , Barbara Wohlmuth View a PDF of the paper titled Analysis of a dilute polymer model with a time-fractional derivative, by Marvin Fritz and Endre S\"uli and Barbara Wohlmuth View PDF HTML (experimental) Abstract: 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 $\alpha \in (\tfrac12,1)$, and derive an energy inequality satisfied by weak solutions. Subjects: Analysis of PDEs (math.AP) MSC classes: 35Q30, 35Q84, 35R11, 60G22, 82C31, 82D60 Cite as: arXiv:2307.16606 [math.AP] (or arXiv:2307.16606v1 [math.AP] for this version) https://doi.org/10.48550/arXiv.2307.16606 Focus to learn more arXiv-issued DOI via DataCite Related DOI : https://doi.org/10.1137/23M1590767 Focus to learn more DOI(s) linking to related resources Submission history From: Marvin Fritz [ view email ] [v1] Mon, 31 Jul 2023 12:23:37 UTC (466 KB) Full-text links: Access Paper: View a PDF of the paper titled Analysis of a dilute polymer model with a time-fractional derivative, by Marvin Fritz and Endre S\"uli and Barbara Wohlmuth View PDF HTML (experimental) TeX Source view license Current browse context: math.AP < prev | next > new | recent | 2023-07 Change to browse by: math References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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