Operator approach to linear problems of hydrodynamics

Nikolay D Kopachevsky, Selim G Krein

384 pages, parution le 04/12/2001

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Résumé

This is the first volume of a set of two devoted to the operator approach to linear problems in hydrodynamics. It presents functional analytical methods applied to the study of small movements and normal oscillations of hydromechanical systems having cavities filled with either ideal or viscous fluids. The work is a sequel to and at the same time substantially extends the volume Operator Methods in Linear Hydrodynamics: Evolution and Spectral Problems by N.D. Kopachevsky, S.G. Krein and Ngo Zuy Kan, published in 1989 by Nauka in Moscow. It includes several new problems on the oscillations of partially dissipative hydrosystems and the oscillations of visco-elastic or relaxing fluids. The work relies on the authors' and their students' works of the last 30–40 years. The readers are not supposed to be familiar with the methods of functional analysis. In the first part of the present volume, the main facts of linear operator theory relevant to linearized problems of hydrodynamics are summarized, including elements of the theories of distributions, self-adjoint operators in Hilbert spaces and in spaces with an indefinite metric, evolution equations and asymptotic methods for their solutions, the spectral theory of operator pencils. The book is particularly useful for researchers, engineers and students in fluid mechanics and mathematics interested in operator theoretical methods for the analysis of hydrodynamical problems.

Table of Contents

Part I Mathematical Foundations of Linear Hydrodynamics
Chapter 1 Operators On Hilbert Spaces
Chapter 2 Fundamental Spaces and Operators of Linear Hydrodynamics
Part II Motion of Bodies With Cavities Containing Ideal Fluids
Chapter 3 Oscillations of Heavy Ideal Fluid in Stationary and Nonstationary Containers
Chapter 4 Problems on Oscillations of Capillary Fluids and Problems on Hydroelasticity in Immovable Containers
Chapter 5 Other Approaches to Hydrodynamics Problems of Ideal Fluids
Chapter 6 Oscillations of and Ideal Rotating Fluid
Appendix B Remarks and Reference Comments to Part II

Caractéristiques techniques

	PAPIER
Éditeur(s)	Birkhäuser
Auteur(s)	Nikolay D Kopachevsky, Selim G Krein
Parution	04/12/2001
Nb. de pages	384
Format	16,7 x 23,8
Couverture	Relié
Poids	781g
Intérieur	Noir et Blanc
EAN13	9783764354060