Operator approach to linear problems of hydrodynamics 2

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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.