Existence of steady solutions for a model for micropolar electrorheological fluid flows with not globally log--Hölder continuous shear exponent

2021/12/15 by Kaltenbach, Alex, Růžička, Michael · 1 citation
#35J92 #35Q35 #46E35 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2112.08026

Abstract

In this paper, we study the existence of weak solutions to a steady system that describes the motion of a micropolar electrorheological fluid. The constitutive relations for the stress tensors belong to the class of generalized Newtonian fluids. The analysis of this particular problem leads naturally to weighted variable exponent Sobolev spaces. We establish the existence of solutions for a material function p that is log--Hölder continuous and an electric field E for that \vertE\vert² is bounded and smooth. Note that these conditions do not imply that the variable shear exponent p= p∘\vert E\vert² is globally log--Hölder continuous.

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