The Linearization Method in Hydrodynamical Stability Theory
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The Linearization Method in Hydrodynamical Stability Theory

The Linearization Method in Hydrodynamical Stability Theory

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About the Book

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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Product Details
  • ISBN-13: 9780821845288
  • Publisher: American Mathematical Society
  • Publisher Imprint: American Mathematical Society
  • Language: English
  • Weight: 425 gr
  • ISBN-10: 0821845284
  • Publisher Date: 30 Dec 1989
  • Binding: Paperback
  • No of Pages: 170


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The Linearization Method in Hydrodynamical Stability Theory
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The Linearization Method in Hydrodynamical Stability Theory
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