Details

Subject(s)

• Fluid dynamics [Browse]
• Differential equations, Nonlinear—Numerical solutions [Browse]
• Heat—Convection—Mathematical models [Browse]

Series

• Applied mathematical sciences (Springer-Verlag New York Inc.) ; v. 91. [More in this series]
• Applied mathematical sciences ; 91

Summary note

"This book describes the energy method, a powerful technique for deriving nonlinear stability estimates in thermal convection contexts. It includes a very readable introduction to the subject (Chapters 2 to 4), which begins at an elementary level and explains the energy method in great detail, and also covers the current topic of convection in porous media, introducing simple models and then showing how useful stability results can be derived. In addition to the basic explanation, many examples from diverse areas of fluid mechanics are described. The book also mentions new areas where the methods are being used, for example, mathematical biology and finance. Several of the results given are published here for the first time."--BOOK JACKET.

Bibliographic references

Includes bibliographical references (p. [397]-442) and index.

Contents

• 1. Introduction
• 2. Illustration of the energy method
• 3. The Navier-Stokes equations and the Benard problem
• 4. Symmetry, competing effects, and coupling parameters
• 5. Convection problems in a half space
• 6. Generalized energies and the Lyapunov method
• 7. Geophysical problems
• 8. Surface tension driven convection
• 9. Convection in generalized fluids
• 10. Time dependent basic states
• 11. Electrohydrodynamic and magnetohydrodynamic convection
• 12. Ferrohydrodynamic convection
• 13. Reacting viscous fluids
• 14. Multi-component convection diffusion
• 15. Convection in a compressible fluid
• 16. Temperature dependent fluid properties
• 17. Penetrative convection
• 18. Nonlinear stability in ocean circulation models
• 19. Numerical solution of eigenvalue problems
• A. Useful inequalities.

Show 17 more Contents items

ISBN

038700453X (alk. paper)

LCCN

2003053004

OCLC

52295238

RCP

C - S

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