Existence of strong solutions for the Oldroyd model with multivalued right-hand side. (December 2022)

• Record Type: Journal Article
• Authors: Eikmeier, André
• Is Part Of: Nonlinear analysis. Volume 225(2022)
• Publication Date: 2022-12
• Subjects: 47J35 -- 34G25 -- 35R70 -- 35Q35; Oldroyd model -- Viscoelastic fluid -- Nonlinear evolution equation -- Multivalued differential equation -- Differential inclusion -- Existence -- Kakutani fixed-point theorem; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2022.113127
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: The initial value problem for a coupled system is studied. The system consists of a differential inclusion and a differential equation and models the fluid flow of a viscoelastic fluid of Oldroyd type. The set-valued right-hand side of the differential inclusion satisfies certain measurability, continuity and growth conditions. The local existence (and global existence for small data) of a strong solution to the coupled system is shown using a generalisation of Kakutani's fixed-point theorem and applying results from the single-valued case.