Description 
1 online resource (xvi, 399 pages) 
Series 
Series on advances in mathematics for applied sciences ; v. 81 

Series on advances in mathematics for applied sciences ; v. 81

Contents 
1. Mathematical models governing fluid flows stability. 1.1. General mathematical models of thermodynamics. 1.2. Classical mathematical models in thermodynamics of fluids. 1.3. Classical mathematical models in thermodynamics. 1.4. Classical perturbation models. 1.5. Generalized incompressible NavierStokes model  2. Incompressible NavierStokes fluid. 2.1. Back to integral setting; involvement of dynamics and bifurcation. 2.2. Stability in semidynamical systems. 2.3. Perturbations; asymptotic stability; linear stability. 2.4. Linear stability. 2.5. Prodi's linearization principle. 2.6. Estimates for the spectrum of Ã. 2.7. Universal stability criteria  3. Elements of calculus of variations. 3.1. Generalities. 3.2. Direct and inverse problems of calculus of variations. 3.3. Symmetrization of some matricial ordinary differential operators. 3.4. Variational principles for problems (3.3.1)(3.3.7). 3.5. Fourier series solutions for variational problems  4. Variants of the energy method for nonstationary equations. 4.1. Variant based on differentiation of parameters. 4.2. Variant based on simplest symmetric part of operators. 4.3. Variants based on energy splitting  5. Applications to linear Bénard convections. 5.1. Magnetic Bénard convection in a partially ionized fluid. 5.2. Magnetic Bénard convection for a fully ionized fluid. 5.3. Convection in a micropolar fluid bounded by rigid walls. 5.4. Convections governed by ode's with variable coefficients  6. Variational methods applied to linear stability. 6.1. Magnetic Bénard problem with Hall effect. 6.2. Lyapunov method applied to the anisotropic Bénard problem. 6.3. Stability criteria for a quasigeostrophic forced zonal flow. 6.4. Variational principle for problem (5.3.1), (5.3.2). 6.5. TaylorDean problem  7. Applications of the direct method to linear stability. 7.1. Couette flow between two cylinders subject to a magnetic field. 7.2. SoretDufour driven convection. 7.3. Magnetic SoretDufour driven convection. 7.4. Convection in a porous medium. 7.5. Convection in the presence of a dielectrophoretic force. 7.6. Convection in an anisotropic M.H.D. thermodiffusive mixture. 7.7. Inhibition of the thermal convection by a magnetic field. 7.8. Microconvection in a binary layer subject to a strong Soret effect. 7.9. Convection in the layer between the sea bed and the permafrost 
Summary 
This is a comprehensive and selfcontained 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 
Bibliography 
Includes bibliographical references (pages 379399) 
Notes 
Print version record 
Subject 
Fluid mechanics  Mathematics.


Heat  Convection  Mathematics.

Form 
Electronic book

Author 
Palese, Lidia.


World Scientific (Firm)

LC no. 
2009026822 
ISBN 
9789814289573 (electronic bk.) 

9814289574 (electronic bk.) 
