The linearization method in hydrodynamical stability theory
Author(s)
Bibliographic Information
The linearization method in hydrodynamical stability theory
（Translations of mathematical monographs, v. 74）
American Mathematical Society, c1989
- Other Title
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Metod linearizat︠s︡ii v gidrodinamicheskoĭ teorii ustoĭchivosti
Метод линеаризации в гидродинамической теории устойчивости
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Note
Translated from the Russian by J.R. Schulenberger, translation edited by Ben Silver
Description and Table of Contents
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.
Table of Contents
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.
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