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An Introduction to the Mathematical Theory of the Navier-Stokes Equations - Steady-State Problems (Hardcover, 2nd ed. 2011)
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An Introduction to the Mathematical Theory of the Navier-Stokes Equations - Steady-State Problems (Hardcover, 2nd ed. 2011)
Series: Springer Monographs in Mathematics
Expected to ship within 12 - 17 working days
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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)
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