The Linearization Method in Hydrodynamical Stability Theory
Will be published approx. on 30. December 1989
Book
Paperback/Softback
170 pages
978-0-8218-4528-8 (ISBN)
Description
This book presents the theory of the linearization method as applied to the problem of steady-state and periodic motions of continuous media. The author proves infinite-dimensional analogues of Lyapunov's theorems on stability, instability, and conditional stability for a large class of continuous media. In addition, semigroup properties for the linearized Navier-Stokes equations in the case of an incompressible fluid are studied, and coercivity inequalities and completeness of a system of small oscillations are proved.
More details
Series
Language
English
Place of publication
Providence
United States
Target group
Professional and scholarly
College/higher education
Weight
425 gr
ISBN-13
978-0-8218-4528-8 (9780821845288)
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Schweitzer Classification
Content
Estimates of solutions of the linearized Navier-Stokes equations Estimates of integral operators in $L_p$ Some estimates of solutions of evolution equations Estimates of the ""leading derivatives"" of solutions of evolution equations Applications to parabolic equations and imbedding theorems The linearized Navier-Stokes equations An estimate of the resolvent of the linearized Navier-Stokes operator Estimates of the leading derivatives of a solution of the linearized steady-state Navier-Stokes equations Stability of fluid motion Stability of the motion of infinite-dimensional systems Conditions for stability Conditions for instability. Conditional stability Stability of periodic motions Formulation of the problem The problem with initial data A condition for asymptotic stability A condition for instability Conditional stability Stability of auto-oscillatory regimes Instability of cycles Damping of the leading derivatives.