This is a comprehensive and self-contained introduction to the mathematical problems of thermal convection. The book delineates the main ideas leading to the authors' variant of the energy method. These can be also applied to other variants of the energy method. The importance of the book lies in its focussing on the best concrete results known in the domain of fluid flows stability and in the systematic treatment of mathematical instruments used in order to reach them.

• Mathematical Models Governing Fluid Flows Stability
• Incompressible Navier-Stokes Fluid
• Elements of Calculus of Variations
• Variants of the Energy Method for Non-Stationary Equations
• Applications to Linear Bénard Convections
• Variational Methods Applied to Linear Stability
• Applications of the Direct Method to Linear Stability

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