The main topics presented in this book deal with methods from functional
analysis applied to the study ofsmall movements and normal oscillations
ofhydrome- chanical systems having cavities filled with either ideal or
viscous fluids. The book is a sequel to and at the same time
substantially extends the volume entitled "Opera- tor Methods in Linear
Hydrodynamics: Evolution and Spectral Problems," by N. D. Kopachevsky,
S.G. Krein, and Ngo Zuy Kan that was published in 1989 by the Nauka
publishing house in Moscow. The present book includesseveral new
problems on the oscillations ofpartially dissipative hydrosystems and
the oscillations of visco-elastic or relaxing fluids. The contents of
this book do not overlap almost at all with the ones in the following
volumes: "Mathematical Problems of the Motion of Viscous Incopressible
Fluids," by O. A. Ladyzhenskaya, "The Dynamics ofBodies with Cavities
Filled with Fluids," by N. N. Moiseev and V. V. Rumiantzev,
"Navier-Stokes Equations," by R. Temam, and "Boundary Problems for
Navier-Stokes Equations," by S. M. Belonosov and K. A. Chernous. Mainly,
the contents of the present book rely on the authors' and their
students' works. We would like to express our gratitude to I. T. Gohberg
and A. S. Markus, who encouraged us to publish the book and who offered
many helpful suggestions. Our gratidude goes also to our colleagues T.
Ya. Azizov, O. A. Ladyzhenskaya, N. N.