Translations of Mathematical Monographs 1989; 170 pp; softcover Volume: 74 Reprint/Revision History: reprinted 1991 ISBN10: 0821845284 ISBN13: 9780821845288 List Price: US$71 Member Price: US$56.80 Order Code: MMONO/74
 This book presents the theory of the linearization method as applied to the problem of steadystate and periodic motions of continuous media. The author proves infinitedimensional 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 NavierStokes 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 NavierStokes 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 NavierStokes equations
 An estimate of the resolvent of the linearized NavierStokes operator
 Estimates of the leading derivatives of a solution of the linearized steadystate NavierStokes equations
 Stability of fluid motion
 Stability of the motion of infinitedimensional 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 autooscillatory regimes
 Instability of cycles
 Damping of the leading derivatives
