eBook ISBN:  9781470410605 
Product Code:  MEMO/226/1060.E 
List Price:  $72.00 
MAA Member Price:  $64.80 
AMS Member Price:  $43.20 
eBook ISBN:  9781470410605 
Product Code:  MEMO/226/1060.E 
List Price:  $72.00 
MAA Member Price:  $64.80 
AMS Member Price:  $43.20 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 226; 2013; 89 ppMSC: Primary 35; 76; 74
The authors study the unconstrained (free) motion of an elastic solid \(\mathcal B\) in a NavierStokes liquid \(\mathcal L\) occupying the whole space outside \(\mathcal B\), under the assumption that a constant body force \(\mathfrak b\) is acting on \(\mathcal B\). More specifically, the authors are interested in the steady motion of the coupled system \(\{\mathcal B,\mathcal L\}\), which means that there exists a frame with respect to which the relevant governing equations possess a timeindependent solution. The authors prove the existence of such a frame, provided some smallness restrictions are imposed on the physical parameters, and the reference configuration of \(\mathcal B\) satisfies suitable geometric properties.

Table of Contents

Chapters

1. Introduction

2. Notation and Preliminaries

3. Steady Free Motion: Definition and Formulation of the Problem

4. Main Result

5. Approximating Problem in Bounded Domains

6. Proof of Main Theorem

7. Bodies with Symmetry

A. Isolated Orientation


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The authors study the unconstrained (free) motion of an elastic solid \(\mathcal B\) in a NavierStokes liquid \(\mathcal L\) occupying the whole space outside \(\mathcal B\), under the assumption that a constant body force \(\mathfrak b\) is acting on \(\mathcal B\). More specifically, the authors are interested in the steady motion of the coupled system \(\{\mathcal B,\mathcal L\}\), which means that there exists a frame with respect to which the relevant governing equations possess a timeindependent solution. The authors prove the existence of such a frame, provided some smallness restrictions are imposed on the physical parameters, and the reference configuration of \(\mathcal B\) satisfies suitable geometric properties.

Chapters

1. Introduction

2. Notation and Preliminaries

3. Steady Free Motion: Definition and Formulation of the Problem

4. Main Result

5. Approximating Problem in Bounded Domains

6. Proof of Main Theorem

7. Bodies with Symmetry

A. Isolated Orientation