ISBN: 3540413855
TITLE: Lecture Notes in Mathematics, Vol.1748
AUTHOR:
TOC:

Introduction vii
Contents xv
1 Modeling of Electrorheological Fluids 1
1.1 General Balance Laws 1
1.2 Electrorheological Fluids 9
1.3 Linear Models for the Stress Tensor T 15
1.3.1 Compressible Electrorheological Fluids 18
1.3.2 Incompressible Electrorheological Fluids 20
1.3.3 Mechanically Incompressible but Electrically Compressible Electrorheological Fluids 21
1.4 Shear Dependent Electrorheological Fluids 24
2 Mathematical Framework 39
2.1 Setting of the Problem and Introduction 39
2.2 Function Spaces 43
2.3 Maxwell's Equations 54
3 Electrorheological Fluids with Shear Dependent Viscosities: Steady Flows 61
3.1 Introduction 61
3.2 Weak Solutions 61
3.3 Strong Solutions 62
3.3.1 Approximations 74
3.4 Existence of Approximate Solutions 84
3.5 Limiting Process A -> infinity 93
3.6 Limiting Process epsylon -> 0 101
4 Electrorheological Fluids with Shear Dependent Viscosities: Unsteady Flows 105
4.1 Setting of the Problem and Main Results 105
4.1.1 Approximations 110
4.2 Existence of Approximate Solutions 114
4.3 Limiting Process A -> infinity 126
4.4 Limiting Process epsylon -> 0 142
5 Appendix 153
5.1 General Auxiliary Results 153
5.2 Auxiliary Results for the Approximations 158
References 165
Index 175
END
