The Navier-Stokes Equations
An Elementary Functional Analytic Approach
Seiten
2012
|
2001
Springer Basel (Verlag)
978-3-0348-0550-6 (ISBN)
Springer Basel (Verlag)
978-3-0348-0550-6 (ISBN)
This book develops an elementary and self-contained approach to the mathematical theory of a viscous, incompressible fluid in a domain of the Euclidean space, described by the equations of Navier-Stokes.
The primary objective of this monograph is to develop an elementary and se- containedapproachtothemathematicaltheoryofaviscousincompressible?uid n in a domain ? of the Euclidean spaceR , described by the equations of Navier- Stokes. The book is mainly directed to students familiar with basic functional analytic tools in Hilbert and Banach spaces. However, for readers' convenience, in the ?rst two chapters we collect, without proof some fundamental properties of Sobolev spaces, distributions, operators, etc. Another important objective is to formulate the theory for a completely general domain ?. In particular, the theory applies to arbitrary unbounded, non-smooth domains. For this reason, in the nonlinear case, we have to restrict ourselves to space dimensions n=2,3 that are also most signi?cant from the physical point of view. For mathematical generality, we will develop the l- earized theory for all n? 2. Although the functional-analytic approach developed here is, in principle, known to specialists, its systematic treatment is not available, and even the diverseaspectsavailablearespreadoutintheliterature.However,theliterature is very wide, and I did not even try to include a full list of related papers, also because this could be confusing for the student. In this regard, I would like to apologize for not quoting all the works that, directly or indirectly, have inspired this monograph.
The primary objective of this monograph is to develop an elementary and se- containedapproachtothemathematicaltheoryofaviscousincompressible?uid n in a domain ? of the Euclidean spaceR , described by the equations of Navier- Stokes. The book is mainly directed to students familiar with basic functional analytic tools in Hilbert and Banach spaces. However, for readers' convenience, in the ?rst two chapters we collect, without proof some fundamental properties of Sobolev spaces, distributions, operators, etc. Another important objective is to formulate the theory for a completely general domain ?. In particular, the theory applies to arbitrary unbounded, non-smooth domains. For this reason, in the nonlinear case, we have to restrict ourselves to space dimensions n=2,3 that are also most signi?cant from the physical point of view. For mathematical generality, we will develop the l- earized theory for all n? 2. Although the functional-analytic approach developed here is, in principle, known to specialists, its systematic treatment is not available, and even the diverseaspectsavailablearespreadoutintheliterature.However,theliterature is very wide, and I did not even try to include a full list of related papers, also because this could be confusing for the student. In this regard, I would like to apologize for not quoting all the works that, directly or indirectly, have inspired this monograph.
Hermann Sohr is professor of mathematics, especially mathematical fluid mechanics, at the University Paderborn, Germany.
Preliminary Results.- The Stationary Navier-Stokes Equations.- The Linearized Nonstationary Theory.- The Full Nonlinear Navier-Stokes Equations.
From the reviews:
"The book is well written and not unnecessarily wordy. There is an up-to-date bibliography and a nice index. ... a mathematician who wishes to know what the important issues concerning eq. (1) are and what has been achieved, would find this an excellent source. Equally, a mathematically-minded student, with a good grounding in analysis and who has decided to work in this area, or the teacher who wants to teach a course on this material would find this a valuable text." (P. N. Shankar,Current Science, Vol. 85 (2), July, 2003)Erscheint lt. Verlag | 14.12.2012 |
---|---|
Reihe/Serie | Modern Birkhäuser Classics |
Zusatzinfo | X, 367 p. |
Verlagsort | Basel |
Sprache | englisch |
Maße | 155 x 235 mm |
Gewicht | 575 g |
Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
Naturwissenschaften ► Physik / Astronomie | |
Schlagworte | Distribution • fluid mechanics • functional analytic approach • Navier-Stokes Equation • Navier-Stokessche Gleichungen • nonstationary linearized theory • Partial differential equations • Serrin's criteria for regularity and uniqueness • Sobolev Space • stationary and nonstationary fluids • viscous incompressible fluids |
ISBN-10 | 3-0348-0550-0 / 3034805500 |
ISBN-13 | 978-3-0348-0550-6 / 9783034805506 |
Zustand | Neuware |
Haben Sie eine Frage zum Produkt? |
Mehr entdecken
aus dem Bereich
aus dem Bereich
Grundlagen, Beispiele, Aufgaben, Lösungen
Buch | Hardcover (2022)
Hanser, Carl (Verlag)
29,99 €