The Energy Method, Stability, and Nonlinear Convection

The Energy Method, Stability, and Nonlinear Convection by Brian Straughan.

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 2-4), which begins at an elementary level and explains the energy method in great detail, and also...

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Bibliographic Details
Main Author: Straughan, Brian (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: New York, NY : Springer New York : Imprint: Springer, 2004.
Edition:2nd ed. 2004.
Series:Applied Mathematical Sciences, 91
Springer eBook Collection.
Subjects:
Applied mathematics.
Engineering mathematics.
Statistical physics.
Dynamical systems.
Dynamics.
Ergodic theory.
Fluids.
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
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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