Overview

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.

Full Product Details

Author:   Nikolay D. Kopachevskii ,  Selim G. Krein
Publisher:   Birkhauser Verlag AG
Imprint:   Birkhauser Verlag AG
Edition:   2001 ed.
Volume:   128
Dimensions:   Width: 15.50cm , Height: 2.30cm , Length: 23.50cm
Weight:   1.660kg
ISBN:  

9783764354060

ISBN 10:   3764354062
Pages:   384
Publication Date:   01 September 2001
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

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

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