Skip to main content
SpringerLink
Log in

The Energy Method, Stability, and Nonlinear Convection

  • Book
  • © 1992

Overview

Authors:
  1. Brian Straughan

    1. Department of Mathematics, University of Glasgow, Glasgow, UK

    View author publications

    You can also search for this author in PubMed   Google Scholar

Part of the book series: Applied Mathematical Sciences (AMS, volume 91)

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 74.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (14 chapters)

  1. Front Matter

    Pages i-xii
    Download chapter PDF

  2. Introduction

    • Brian Straughan
    Pages 1-2

  3. Illustration of the Energy Method on Simple Examples and Discussion of Linear Theory

    • Brian Straughan
    Pages 3-37

  4. The Navier-Stokes Equations, the Boussinesq Approximation, and the Standard Bénard Problem

    • Brian Straughan
    Pages 38-55

  5. Symmetry, Competing Effects, and Coupling Parameters; Multiparameter Eigenvalue Problems; Finite Geometries

    • Brian Straughan
    Pages 56-74

  6. Convection Problems in a Half-Space

    • Brian Straughan
    Pages 75-81

  7. Generalized Energies and the Lyapunov Method

    • Brian Straughan
    Pages 82-107

  8. Geophysical Problems

    • Brian Straughan
    Pages 108-131

  9. Surface Tension Driven Convection

    • Brian Straughan
    Pages 132-144

  10. Convection in Generalized Fluids

    • Brian Straughan
    Pages 145-153

  11. Time Dependent Basic States

    • Brian Straughan
    Pages 154-160

  12. Electrohydrodynamic and Magnetohydrodynamic Convection

    • Brian Straughan
    Pages 161-175

  13. Ferrohydrodynamic Convection

    • Brian Straughan
    Pages 176-189

  14. Convective Instabilities for Reacting Viscous Fluids Far from Equilibrium

    • Brian Straughan
    Pages 190-203

  15. Energy Stability and Other Continuum Theories

    • Brian Straughan
    Pages 204-206

  16. Back Matter

    Pages 207-243
    Download chapter PDF
Back to top

Keywords

About this book

The writing of this book was begun during the academic year 1984-1985 while I was a visiting Associate Professor at the University of Wyoming. I am extremely grateful to the people there for their help, in particular to Dick Ewing, Jack George and Robert Gunn, and to Ken Gross, who is now at the University of Vermont. A major part of the first draft of this book was written while I was a visiting Professor at the University of South Carolina during the academic year 1988-1989. I am indebted to the people there for their help, in one way or another, particularly to Ron DeVore, Steve Dilworth, Bob Sharpley, Dave Walker, and especially to the chairman of the Mathematics Department at the University of South Carolina, Colin Bennett. I also wish to express my sincere gratitude to Ray Ogden and Profes­ sor I.N. Sneddon, F.R.S., both of Glasgow University, for their help over a number of years. I also wish to record my thanks to Ron Hills and Paul Roberts, F.R.S., for giving me a copy of their paper on the Boussinesq ap­ proximation prior to publication and for allowing me to describe their work here. I should like to thank my Ph.D. student Geoff McKay for spotting several errors and misprints in an early draft. Finally, I am very grateful to an anonymous reviewer for several pertinent suggestions regarding the energy-Casimir method.

Reviews

From the reviews of the second edition:

"This application-oriented book is a revised edition … more definitions, new interpretations and new results are included, some chapters are enlarged, 6 chapters are added. … the presentation is very clear, making the book useful to undergraduate and graduate students in applied mathematics too. … The main text and the very rich list of references reflect the interests and results of the author and his collaborators. The book makes a good contribution to the literature on stability of fluid flows … ." (Adelina Georgescu, Mathematical Reviews, 2004i)

Authors and Affiliations

  • Department of Mathematics, University of Glasgow, Glasgow, UK

    Brian Straughan

Bibliographic Information

Publish with us

Policies and ethics

Back to top

Search

Navigation