Fundamentals of stability in thermo-hydrodynamics

Stability as defined by Liapunov is reviewed for both discrete and continuous systems. Normal modes superposition and the Benard problem of thermal convention are addressed in consideration of the linearized theory. The Orr approach and Serrin-Joseph theory are presented as examples of energy methods. Liapunov's theorems and examples of his functions are examined as well as the Gorkov-Malkus-Veronis power series and the Stuart perturbation methods. General conditions for existence of a variational principle, the variational principle for the Bernard linearized problem, a reformulation of Serrin-Joseph's principle, and numerical procedure for variational methods are also discussed.