Operator Approach to Linear Problems of Hydrodynamics

1. Front Matter

   Pages i-xxiv

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2. Introduction

   1. Introduction

      • Nikolay D. Kopachevsky, Selim G. Krein

      Pages 1-3

3. Motion of Bodies with Cavities Containing Viscous Incompressible Fluids

   1. Front Matter

      Pages 5-5

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   2. Motion of Bodies with Cavities Completely Filled with Viscous Incompressible Fluids

      • Nikolay D. Kopachevsky, Selim G. Krein

      Pages 7-66

   3. Motion of Viscous Fluids in Open Containers

      • Nikolay D. Kopachevsky, Selim G. Krein

      Pages 67-186

   4. Oscillations of Capillary Viscous Fluids

      • Nikolay D. Kopachevsky, Selim G. Krein

      Pages 187-235

4. Back Matter

   Pages 237-247

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5. Small Oscillations of Complex Hydrodynamic Systems

   1. Front Matter

      Pages 249-250

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   2. Oscillations of Partially Dissipative Hydrosystems

      • Nikolay D. Kopachevsky, Selim G. Krein

      Pages 251-314

   3. Oscillations of Visco-Elastic and Relaxing Media

      • Nikolay D. Kopachevsky, Selim G. Krein

      Pages 315-410

6. Back Matter

   Pages 411-414

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7. Back Matter

   Pages 415-444

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As mentioned in the Introduction to Volume I, the present monograph is intended both for mathematicians interested in applications of the theory of linear operators and operator-functions to problems of hydrodynamics, and for researchers of applied hydrodynamic problems, who want to study these problems by means of the most recent achievements in operator theory. The second volume considers nonself-adjoint problems describing motions and normal oscillations of a homogeneous viscous incompressible fluid. These ini­ tial boundary value problems of mathematical physics include, as a rule, derivatives in time of the unknown functions not only in the equation, but in the boundary conditions, too. Therefore, the spectral problems corresponding to such boundary value problems include the spectral parameter in the equation and in the bound­ ary conditions, and are nonself-adjoint. In their study, we widely used the theory of nonself-adjoint operators acting in a Hilbert space and also the theory of operator pencils. In particular, the methods of operator pencil factorization and methods of operator theory in a space with indefinite metric find here a wide application. We note also that this volume presents both the now classical problems on oscillations of a homogeneous viscous fluid in an open container (in an ordinary state and in weightlessness) and a new set of problems on oscillations of partially dissipative hydrodynamic systems, and problems on oscillations of a visco-elastic or relaxing fluid. Some of these problems need a more careful additional investigation and are rather complicated.

• Hydrodynamics
• fluid mechanics
• functional analysis
• mechanics
• operator
• fluid- and aerodynamics

• Mathematical Department, Taurida National V. Vernadsky University, Simferopol, Ukraine

  Nikolay D. Kopachevsky

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