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The book provides a comprehensive, detailed and self-contained
treatment of the fundamental mathematical properties of
boundary-value problems related to the Navier-Stokes equations.
These properties include existence, uniqueness and regularity of
solutions in bounded as well as unbounded domains. Whenever the
domain is unbounded, the asymptotic behavior of solutions is also
investigated. This book is the new edition of the original two
volume book, under the same title, published in 1994. In this new
edition, the two volumes have merged into one and two more chapters
on steady generalized oseen flow in exterior domains and steady
Navier-Stokes flow in three-dimensional exterior domains have been
added. Most of the proofs given in the previous edition were also
updated. An introductory first chapter describes all relevant
questions treated in the book and lists and motivates a number of
significant and still open questions. It is written in an
expository style so as to be accessible also to
non-specialists.Each chapter is preceded by a substantial,
preliminary discussion of the problems treated, along with their
motivation and the strategy used to solve them. Also, each chapter
ends with a section dedicated to alternative approaches and
procedures, as well as historical notes. The book contains more
than 400 stimulating exercises, at different levels of difficulty,
that will help the junior researcher and the graduate student to
gradually become accustomed with the subject. Finally, the book is
endowed with a vast bibliography that includes more than 500 items.
Each item brings a reference to the section of the book where it is
cited. The book will be useful to researchers and graduate students
in mathematics in particular mathematical fluid mechanics and
differential equations. Review of First Edition, First Volume: "The
emphasis of this book is on an introduction to the mathematical
theory of the stationary Navier-Stokes equations. It is written in
the style of a textbook and is essentially self-contained. The
problems are presented clearly and in an accessible manner. Every
chapter begins with a good introductory discussion of the problems
considered, and ends with interesting notes on different approaches
developed in the literature. Further, stimulating exercises are
proposed. (Mathematical Reviews, 1995)
This is the second of four volumes on the Navier-Stokes equations,
specifically on Nonlinear Stationary Problems. The volumes deal
with the fundamental mathematical properties of the Navier-Stokes
equations, such as existence, regularity and uniqueness of
solutions, and, for unbounded domains, their asymptotic behavior.
The work is an up-to-date and detailed investigation of these
problems for motions in domains of different types: bounded,
exterior and domain with noncompact boundaries. Throughout the
work, main problems which, so far, remain open are pointed out and
for some of these conjectures are offered. New results are
presented throughout, while several classical subjects are treated
in a completely original way. The work is mathematically self
contained, requiring no specific background. The 200-plus exercises
along with the chapter summaries and questions make this an
excellent textbook for any theoretical Fluid Mechanics course; it
is suitable as well for self teaching. It is set up to remain
useful as a reference or dictionary.
The content of the volume is constituted by four articles. The
first concerns the theory of propagation of plane waves in elastic
media. The second treats theoretically the linear, weakly
non-linear, and non-linear stability of flows of a viscous
incompressible fluid in a diverging channel. The third lecture
investigates the mathematical properties of the equations governing
the motion of a viscous incompressible second-grade fluid, such as
existence, uniqueness of classical solutions and stability of
steady-state flows. The last lecture provides some basic results on
wave propagation in continuum models. The objective of this book is
to emphasize and to compare the various aspects of interest which
include the necessary mathematical background, constitutive
theories for material of differential type, polarized and shock
waves, and second sound in solids at low temperatures.
The book provides a comprehensive, detailed and self-contained
treatment of the fundamental mathematical properties of
boundary-value problems related to the Navier-Stokes equations.
These properties include existence, uniqueness and regularity of
solutions in bounded as well as unbounded domains. Whenever the
domain is unbounded, the asymptotic behavior of solutions is also
investigated. This book is the new edition of the original two
volume book, under the same title, published in 1994. In this new
edition, the two volumes have merged into one and two more chapters
on steady generalized oseen flow in exterior domains and steady
Navier-Stokes flow in three-dimensional exterior domains have been
added. Most of the proofs given in the previous edition were also
updated. An introductory first chapter describes all relevant
questions treated in the book and lists and motivates a number of
significant and still open questions. It is written in an
expository style so as to be accessible also to
non-specialists.Each chapter is preceded by a substantial,
preliminary discussion of the problems treated, along with their
motivation and the strategy used to solve them. Also, each chapter
ends with a section dedicated to alternative approaches and
procedures, as well as historical notes. The book contains more
than 400 stimulating exercises, at different levels of difficulty,
that will help the junior researcher and the graduate student to
gradually become accustomed with the subject. Finally, the book is
endowed with a vast bibliography that includes more than 500 items.
Each item brings a reference to the section of the book where it is
cited. The book will be useful to researchers and graduate students
in mathematics in particular mathematical fluid mechanics and
differential equations. Review of First Edition, First Volume: "The
emphasis of this book is on an introduction to the mathematical
theory of the stationary Navier-Stokes equations. It is written in
the style of a textbook and is essentially self-contained. The
problems are presented clearly and in an accessible manner. Every
chapter begins with a good introductory discussion of the problems
considered, and ends with interesting notes on different approaches
developed in the literature. Further, stimulating exercises are
proposed. (Mathematical Reviews, 1995)
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