Abstract
AbstractIn 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 $${\hat{p}}$$
p
^
that is $$\log $$
log
-Hölder continuous and an electric field $$\textbf{E}$$
E
for that $$\vert \textbf{E}\vert ^2$$
|
E
|
2
is bounded and smooth. Note that these conditions do not imply that the variable shear exponent $$p={\hat{p}}\circ \vert \textbf{E}\vert ^2$$
p
=
p
^
∘
|
E
|
2
is globally $$\log $$
log
-Hölder continuous.
Funder
Albert-Ludwigs-Universität Freiburg im Breisgau
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computational Mathematics,Condensed Matter Physics,Mathematical Physics
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