Hydrodynamic stability theory

A. Georgescu (Autor)

Buch | Softcover

300 Seiten

2010 | Softcover reprint of the original 2nd ed. 1985
Springer (Verlag)
978-90-481-8289-3 (ISBN)

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The great number of varied approaches to hydrodynamic stability theory appear as a bulk of results whose classification and discussion are well-known in the literature. Several books deal with one aspect of this theory alone (e.g. the linear case, the influence of temperature and magnetic field, large classes of globally stable fluid motions etc.). The aim of this book is to provide a complete mathe matical treatment of hydrodynamic stability theory by combining the early results of engineers and applied mathematicians with the recent achievements of pure mathematicians. In order to ensure a more operational frame to this theory I have briefly outlined the main results concerning the stability of the simplest types of flow. I have attempted several definitions of the stability of fluid flows with due consideration of the connections between them. On the other hand, as the large number of initial and boundary value problems in hydrodynamic stability theory requires appropriate treat ments, most of this book is devoted to the main concepts and methods used in hydrodynamic stability theory. Open problems are expressed in both mathematical and physical terms.

1. Classical hydrodynamic stability.- 2. Generalized solutions in hydrodynamic stability.- 3. Branching and stability of the solutions of the Navier-Stokes equations.- 4. Nature of turbulence.- 5. The influence of the presence of a porous medium on hydrodynamic stability.- Appendices 1. Operators in Hilbert spaces.- 2. Semigroups of operators in Banach spaces.- 3. Spectral theory of linear operators.- 4. Calculus of variations.- 5. Geometric methods in branching theory.- 6. New methods for solving the Orr-Sommerfeld equation.- 7. Analytical methods to solve some eigenvalue problems in hydrodynamic and hydromagnetic stability theory.- 8. Stability of nonstationary fluid flows.- Afterword.

Erscheint lt. Verlag	30.12.2010
Reihe/Serie	Mechanics: Analysis ; 9
Zusatzinfo	VII, 300 p.
Verlagsort	Dordrecht
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Themenwelt	Naturwissenschaften ► Physik / Astronomie ► Mechanik
ISBN-10	90-481-8289-1 / 9048182891
ISBN-13	978-90-481-8289-3 / 9789048182893
Zustand	Neuware