Operator Approach to Linear Problems of Hydrodynamics

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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.