Nikolaj D. Kopac evskij Boeken

This monograph targets mathematicians interested in applying linear operator theory to hydrodynamics and researchers exploring applied hydrodynamic issues through recent advancements in operator theory. The second volume focuses on nonself-adjoint problems related to the motions and normal oscillations of a homogeneous viscous incompressible fluid. These initial boundary value problems in mathematical physics typically involve time derivatives of unknown functions in both the equations and boundary conditions, leading to spectral problems that are nonself-adjoint due to the spectral parameter's presence in both the equations and boundary conditions. The study employs the theory of nonself-adjoint operators within a Hilbert space and operator pencils, utilizing methods such as operator pencil factorization and techniques in spaces with indefinite metrics. This volume covers classical problems regarding oscillations of a homogeneous viscous fluid in open containers, including scenarios in weightlessness, as well as new challenges concerning oscillations in partially dissipative hydrodynamic systems and visco-elastic or relaxing fluids. Some of these problems require further investigation due to their complexity.

This monograph targets mathematicians interested in applying linear operators and operator-functions to hydrodynamic problems, as well as researchers seeking to explore these issues through recent advancements in operator theory. The second volume addresses nonself-adjoint problems related to the motions and normal oscillations of a homogeneous viscous incompressible fluid. These initial boundary value problems typically involve time derivatives of unknown functions in both the equations and boundary conditions, leading to spectral problems that include the spectral parameter in both the equations and boundary conditions, thus being nonself-adjoint. The study extensively employs the theory of nonself-adjoint operators in Hilbert spaces and operator pencils, utilizing methods such as operator pencil factorization and techniques in spaces with indefinite metrics. This volume encompasses classical problems concerning oscillations of a homogeneous viscous fluid in open containers (both in normal conditions and weightlessness) and introduces new challenges related to oscillations in partially dissipative hydrodynamic systems, as well as visco-elastic or relaxing fluids. Some of these issues require further detailed investigation and are notably complex.

InhaltsverzeichnisI: 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.List of Symbols.