Ebook: Operator Approach to Linear Problems of Hydrodynamics: Volume 1: Self-adjoint Problems for an Ideal Fluid

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.

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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.
Content:
Front Matter....Pages i-xxiv
Introduction....Pages 1-3
Front Matter....Pages 5-5
Operators on Hilbert Spaces....Pages 7-108
Fundamental Spaces and Operators of Linear Hydrodynamics....Pages 109-141
Front Matter....Pages 149-149
Oscillations of a Heavy Ideal Fluid in Stationary and Nonstationary Containers....Pages 151-197
Problems on Oscillations of Capillary Fluids and Problems on Hydroelasticity in Immovable Containers....Pages 199-248
Other Operator Approaches to Hydrodynamics Problems of Ideal Fluids....Pages 249-279
Oscillations of an Ideal Rotating Fluid....Pages 281-343
Back Matter....Pages 355-384

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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.
Content:
Front Matter....Pages i-xxiv
Introduction....Pages 1-3
Front Matter....Pages 5-5
Operators on Hilbert Spaces....Pages 7-108
Fundamental Spaces and Operators of Linear Hydrodynamics....Pages 109-141
Front Matter....Pages 149-149
Oscillations of a Heavy Ideal Fluid in Stationary and Nonstationary Containers....Pages 151-197
Problems on Oscillations of Capillary Fluids and Problems on Hydroelasticity in Immovable Containers....Pages 199-248
Other Operator Approaches to Hydrodynamics Problems of Ideal Fluids....Pages 249-279
Oscillations of an Ideal Rotating Fluid....Pages 281-343
Back Matter....Pages 355-384
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