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Electrorheological Fluids: Modeling and Mathematical Theory

  • Book
  • © 2000

Overview

Authors:
  1. Michael Růžička
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1748)

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Table of contents (4 chapters)

  1. Front Matter

    Pages i-xv
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  2. Modeling of electrorheological fluids

    • Michael Růžička
    Pages 1-37

  3. Mathematical framework

    • Michael Růžička
    Pages 39-59

  4. Electrorheological fluids with shear dependent viscosities: Steady flows

    • Michael Růžička
    Pages 61-103

  5. Electrorheological fluids with shear dependent viscosities: Unsteady flows

    • Michael Růžička
    Pages 105-151

  6. Back Matter

    Pages 153-176
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Keywords

About this book

This is the first book to present a model, based on rational mechanics of electrorheological fluids, that takes into account the complex interactions between the electromagnetic fields and the moving liquid. Several constitutive relations for the Cauchy stress tensor are discussed. The main part of the book is devoted to a mathematical investigation of a model possessing shear-dependent viscosities, proving the existence and uniqueness of weak and strong solutions for the steady and the unsteady case. The PDS systems investigated possess so-called non-standard growth conditions. Existence results for elliptic systems with non-standard growth conditions and with a nontrivial nonlinear r.h.s. and the first ever results for parabolic systems with a non-standard growth conditions are given for the first time. Written for advanced graduate students, as well as for researchers in the field, the discussion of both the modeling and the mathematics is self-contained.

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