Operator Approach to Linear Problems of Hydrodynamics

Selim G. Krein

ISBN 10: 3764354062 / ISBN 13: 9783764354060

Published by Birkhäuser Basel, Springer Basel Sep 2001, 2001

About this Item

This item is printed on demand - Print on Demand Titel. Neuware -The main topics presented in this book deal with methods from functional analysis applied to the study ofsmall movements and normal oscillations ofhydrome chanical systems having cavities filled with either ideal or viscous fluids. The book is a sequel to and at the same time substantially extends the volume entitled 'Opera tor Methods in Linear Hydrodynamics: Evolution and Spectral Problems,' by N. D. Kopachevsky, S.G. Krein, and Ngo Zuy Kan that was published in 1989 by the Nauka publishing house in Moscow. The present book includesseveral new problems on the oscillations ofpartially dissipative hydrosystems and the oscillations of visco-elastic or relaxing fluids. The contents of this book do not overlap almost at all with the ones in the following volumes: 'Mathematical Problems of the Motion of Viscous Incopressible Fluids,' by O. A. Ladyzhenskaya, 'The Dynamics ofBodies with Cavities Filled with Fluids,' by N. N. Moiseev and V. V. Rumiantzev, 'Navier-Stokes Equations,' by R. Temam, and 'Boundary Problems for Navier-Stokes Equations,' by S. M. Belonosov and K. A. Chernous. Mainly, the contents of the present book rely on the authors' and their students' works. We would like to express our gratitude to I. T. Gohberg and A. S. Markus, who encouraged us to publish the book and who offered many helpful suggestions. Our gratidude goes also to our colleagues T. Ya. Azizov, O. A. Ladyzhenskaya, N. N.Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin 412 pp. Englisch.

Seller Inventory # 9783764354060

Bibliographic Details

• Title: Operator Approach to Linear Problems of Hydrodynamics
• Publisher: Birkhäuser Basel, Springer Basel Sep 2001
• Publication Date: 2001
• Language: English
• ISBN 10: 3764354062
• ISBN 13: 9783764354060
• Binding: Buch
• Condition: Neu
• Dimensions: 241W x 160H x 28D millimeters 241 millimeters width by 160 millimeters height by 28 millimeters depth
• Weight: 781 grams

About this title

Synopsis

The main topics presented in this book deal with methods from functional analysis applied to the study ofsmall movements and normal oscillations ofhydrome- chanical systems having cavities filled with either ideal or viscous fluids. The book is a sequel to and at the same time substantially extends the volume entitled "Opera- tor Methods in Linear Hydrodynamics: Evolution and Spectral Problems," by N. D. Kopachevsky, S.G. Krein, and Ngo Zuy Kan that was published in 1989 by the Nauka publishing house in Moscow. The present book includesseveral new problems on the oscillations ofpartially dissipative hydrosystems and the oscillations of visco-elastic or relaxing fluids. The contents of this book do not overlap almost at all with the ones in the following volumes: "Mathematical Problems of the Motion of Viscous Incopressible Fluids," by O. A. Ladyzhenskaya, "The Dynamics ofBodies with Cavities Filled with Fluids," by N. N. Moiseev and V. V. Rumiantzev, "Navier-Stokes Equations," by R. Temam, and "Boundary Problems for Navier-Stokes Equations," by S. M. Belonosov and K. A. Chernous. Mainly, the contents of the present book rely on the authors' and their students' works. We would like to express our gratitude to I. T. Gohberg and A. S. Markus, who encouraged us to publish the book and who offered many helpful suggestions. Our gratidude goes also to our colleagues T. Ya. Azizov, O. A. Ladyzhenskaya, N. N.

Synopsis

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.