The linearization method in hydrodynamical stability theory
著者
書誌事項
The linearization method in hydrodynamical stability theory
（Translations of mathematical monographs, v. 74）
American Mathematical Society, c1989
- タイトル別名
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Metod linearizat︠s︡ii v gidrodinamicheskoĭ teorii ustoĭchivosti
Метод линеаризации в гидродинамической теории устойчивости
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注記
Translated from the Russian by J.R. Schulenberger, translation edited by Ben Silver
内容説明・目次
内容説明
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.
目次
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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