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Operator Approach to Linear Problems of Hydrodynamics - Volume 2: Nonself-adjoint Problems for Viscous Fluids (Hardcover, 2003 ed.)
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Operator Approach to Linear Problems of Hydrodynamics - Volume 2: Nonself-adjoint Problems for Viscous Fluids (Hardcover, 2003 ed.)
Series: Operator Theory: Advances and Applications, 146
Expected to ship within 10 - 15 working days
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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."
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