Energy Method, Stability, and Nonlinear Convection

• 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.

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)