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Mathematical Theory of Incompressible Nonviscous Fluids - Taschenbuch

2011, ISBN: 1461287227

[EAN: 9781461287223], Neubuch, [SC: 0.0], [PU: Springer New York], DERIVATION; INVARIANT; DIFFERENTIAL EQUATION; FLUID DYNAMICS; FUNCTION; FUNCTIONAL ANALYSIS; MEASURE; PROOF; THEOREM, Dr… Mehr…

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Mathematical Theory of Incompressible Nonviscous Fluids (Paperback) - Taschenbuch

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Fluid dynamics is an ancient science incredibly alive today. Modern technol­ ogy and new needs require a deeper knowledge of the behavior of real fluids, and new discoveries or steps… Mehr…

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Carlo Marchioro; Mario Pulvirenti:
Mathematical Theory of Incompressible Nonviscous Fluids - Taschenbuch

2011, ISBN: 9781461287223

Buch, Softcover, Softcover reprint of the original 1st ed. 1994, [PU: Springer-Verlag New York Inc.], Springer-Verlag New York Inc., 2011

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Marchioro, Carlo; Pulvirenti, Mario:
Mathematical Theory of Incompressible Nonviscous Fluids - Taschenbuch

2011, ISBN: 1461287227

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Details zum Buch
Mathematical Theory of Incompressible Nonviscous Fluids

Fluid dynamics is an ancient science incredibly alive today. Modern technol­ ogy and new needs require a deeper knowledge of the behavior of real fluids, and new discoveries or steps forward pose, quite often, challenging and diffi­ cult new mathematical {::oblems. In this framework, a special role is played by incompressible nonviscous (sometimes called perfect) flows. This is a mathematical model consisting essentially of an evolution equation (the Euler equation) for the velocity field of fluids. Such an equation, which is nothing other than the Newton laws plus some additional structural hypo­ theses, was discovered by Euler in 1755, and although it is more than two centuries old, many fundamental questions concerning its solutions are still open. In particular, it is not known whether the solutions, for reasonably general initial conditions, develop singularities in a finite time, and very little is known about the long-term behavior of smooth solutions. These and other basic problems are still open, and this is one of the reasons why the mathe­ matical theory of perfect flows is far from being completed. Incompressible flows have been attached, by many distinguished mathe­ maticians, with a large variety of mathematical techniques so that, today, this field constitutes a very rich and stimulating part of applied mathematics.

Detailangaben zum Buch - Mathematical Theory of Incompressible Nonviscous Fluids


EAN (ISBN-13): 9781461287223
ISBN (ISBN-10): 1461287227
Gebundene Ausgabe
Taschenbuch
Erscheinungsjahr: 2011
Herausgeber: Springer-Verlag New York Inc.

Buch in der Datenbank seit 2014-10-09T22:44:25+02:00 (Berlin)
Detailseite zuletzt geändert am 2024-03-13T10:28:08+01:00 (Berlin)
ISBN/EAN: 1461287227

ISBN - alternative Schreibweisen:
1-4612-8722-7, 978-1-4612-8722-3
Alternative Schreibweisen und verwandte Suchbegriffe:
Autor des Buches: marchi, marchioro, pulvirenti
Titel des Buches: fluids, mathematical


Daten vom Verlag:

Autor/in: Carlo Marchioro; Mario Pulvirenti
Titel: Applied Mathematical Sciences; Mathematical Theory of Incompressible Nonviscous Fluids
Verlag: Springer; Springer US
284 Seiten
Erscheinungsjahr: 2011-09-30
New York; NY; US
Gedruckt / Hergestellt in Niederlande.
Sprache: Englisch
160,49 € (DE)
164,99 € (AT)
177,00 CHF (CH)
POD
XII, 284 p.

BC; Hardcover, Softcover / Mathematik/Analysis; Mathematische Analysis, allgemein; Verstehen; Derivation; Invariant; differential equation; equation; fluid dynamics; function; functional analysis; measure; proof; theorem; Analysis; BB

1 General Considerations on the Euler Equation.- 1.1. The Equation of Motion of an Ideal Incompressible Fluid.- 1.2. Vorticity and Stream Function.- 1.3. Conservation Laws.- 1.4. Potential and Irrotational Flows.- 1.5. Comments.- Appendix 1.1 (Liouville Theorem).- Appendix 1.2 (A Decomposition Theorem).- Appendix 1.3 (Kutta-Joukowski Theorem and Complex Potentials).- Appendix 1.4 (d’Alembert Paradox).- Exercises.- 2 Construction of the Solutions.- 2.1. General Considerations.- 2.2. Lagrangian Representation of the Vorticity.- 2.3. Global Existence and Uniqueness in Two Dimensions.- 2.4. Regularity Properties and Classical Solutions.- 2.5. Local Existence and Uniqueness in Three Dimensions.- 2.6. Some Heuristic Considerations on the Three-Dimensional Motion.- 2.7. Comments.- Appendix 2.1 (Integral Inequalities).- Appendix 2.2 (Some Useful Inequalities).- Appendix 2.3 (Quasi-Lipschitz Estimate).- Appendix 2.4 (Regularity Estimates).- Exercises.- 3 Stability of Stationary Solutions of the Euler Equation.- 3.1. A Short Review of the Stability Concept.- 3.2. Sufficient Conditions for the Stability of Stationary Solutions: The Arnold Theorems.- 3.3. Stability in the Presence of Symmetries.- 3.4. Instability.- 3.5. Comments.- Exercises.- 4 The Vortex Model.- 4.1. Heuristic Introduction.- 4.2. Motion of Vortices in the Plane.- 4.3. The Vortex Motion in the Presence of Boundaries.- 4.4. A Rigorous Derivation of the Vortex Model.- 4.5. Three-Dimensional Models.- 4.6. Comments.- Exercises.- 5 Approximation Methods.- 5.1. Introduction.- 5.2. Spectral Methods.- 5.3. Vortex Methods.- 5.4. Comments.- Appendix 5.1 (On K-R Distance).- Exercises.- 6 Evolution of Discontinuities.- 6.1. Vortex Sheet.- 6.2. Existence and Behavior of the Solutions.- 6.3. Comments.- 6.4. SpatiallyInhomogeneous Fluids.- 6.5. Water Waves.- 6.6. Approximations.- Appendix 6.1 (Proof of a Theorem of the Cauchy-Kowalevski Type).- Appendix 6.2 (On Surface Tension).- 7 Turbulence.- 7.1. Introduction.- 7.2. The Onset of Turbulence.- 7.3. Phenomenological Theories.- 7.4. Statistical Solutions and Invariant Measures.- 7.5. Statistical Mechanics of Vortex Systems.- 7.6. Three-Dimensional Models for Turbulence.- References.

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