Table of Contents

1 Introduction.- 2 Illustration of the energy method.- 3 The Navier-Stokes equations and the Bénard 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.- A.1 The Poincaré inequality.- A.2 The Wirtinger inequality.- A.3 The Sobolev inequality.- A.4 An inequality for the supremum of a function.- A.7 A two-dimensional surface inequality.- A.8 Inequality (A.20) is false in three-dimensions.- References.

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2nd edition

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)