Stability criteria for fluid flows / Adelina Georgescu, Lidia Palese.

Format:

Book

Author/Creator:

Georgescu, Adelina.

Contributor:

Palese, Lidia.

Series:

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

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

Language:

English

Subjects (All):

Heat--Convection--Mathematics.

Heat.

Fluid mechanics--Mathematics.

Fluid mechanics.

Physical Description:

1 online resource (418 p.)

Edition:

1st ed.

Place of Publication:

Singapore ; Hackensack, NJ : World Scientific, c2010.

Language Note:

English

Summary:

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. <i>Sample Chapter(s)</i><br>Introduction (121 KB)<br>Chapter 1: Mathematical models governing fluid flows stability (640 KB

Contents:

Contents; Introduction; 1. Mathematical models governing fluid flows stability; 1.1 General mathematical models of thermodynamics; 1.1.1 Physical quantities and their mathematical description; 1.1.2 Global quantities and their integral representation; 1.1.3 Balance equations in integral form; 1.1.4 Balance equations in differential form; 1.1.5 Constitutive equations. State equations; 1.2 Classical mathematical models in thermodynamics of fluids; 1.2.1 Incompressible Navier-Stokes model; 1.2.2 Navier-Stokes-Fourier model and Oberbeck-Boussinesq approximation

1.3 Classical mathematical models in thermodynamics1.4 Classical perturbation models; 1.4.1 Perturbation models; 1.4.2 Perturbation incompressible Navier-Stokes model; 1.4.3 Perturbation model for viscous incompressible homogeneous thermoelectrically conducting or nonconducting fluid; 1.4.3.1 Magnetic case; 1.4.3.2 Perturbation Navier-Stokes-Fourier model in the Oberbeck-Boussinesq approximation; 1.4.4 Perturbation model for viscous incompressible homogeneous thermoelectrically fully ionized conducting fluids

1.4.5 Perturbation model for viscous incompressible homogeneous thermoelectrically partially ionized conducting fluid1.4.6 Perturbation model for a thermally conducting binary mixture in the presence of the Soret and Dufour effects; 1.5 Generalized incompressible Navier-Stokes model; 1.5.1 Generalized models; 1.5.2 Generalized model for strong solutions; 1.5.3 Perturbation generalized model for strong solutions; 2. Incompressible Navier-Stokes 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; 2.4.1 Finite-dimensional case; 2.4.2 Infinite-dimensional case; 2.5 Prodi's linearization principle; 2.6 Estimates for the spectrum of A; 2.6.1 Necessary conditions for belonging to (-A); 2.6.2 Spectrum bounds based on straight lines; 2.6.3 Spectrum bounds based on parabolas; 2.7 Universal stability criteria; 2.7.1 Energy relation; 2.7.2 Three-dimensional case; 2.7.2.1 Incompressible Navier-Stokes uid; 2.7.3 Two-dimensional case; 2.7.3.1 Leray setting; 2.7.3.2 Weak setting

2.7.3.3 A variant of Leray setting. Method based on orthogonal projections2.7.3.4 Su cient criteria for nonexistence of subcritical instabilities; 3. Elements of calculus of variations; 3.1 Generalities; 3.2 Direct and inverse problems of calculus of variations; 3.2.1 Variational problems in classical, generalized and abstract setting; 3.2.2 Construction of the boundary-value problem associated with a variational problem. Necessary conditions for extremum; 3.2.3 Classical Euler equations associated with variational problems for particular functionals

3.2.4 Construction of the variational problem associated with an Euler equation: energy method. Quadratic functionals associated with affine or linear equations

Notes:

Description based upon print version of record.

Includes bibliographical references (p. 379-399).

ISBN:

9786612761690

9781282761698

1282761692

9789814289573

9814289574

OCLC:

630153528