Existence of steady solutions for micropolar electrorheological fluid flows. (September 2015)

• Record Type: Journal Article
• Authors: Ettwein, F.; Růžička, M.; Weber, B.
• Is Part Of: Nonlinear analysis. Volume 125(2015)
• Page Start: 1
• Page End: 29
• Publication Date: 2015-09
• Subjects: Existence of solutions -- Lipschitz truncation -- L∞-truncation -- Weighted function spaces -- Micropolar electrorheological fluids; 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.2015.05.004
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper we study the existence of weak solutions to a steady system describing the motion of micropolar electrorheological fluids. The constitutive relations for the stress tensors belong to the class of generalized Newtonian fluids. The analysis of the problem leads naturally to weighted Sobolev spaces. The emphasis of the paper is devoted to the study of the degenerate problem. Using the Lipschitz truncation and the L ∞ -truncation we derive various lower bounds, depending also on the electric field, ensuring the existence of solutions.