Applied Mathematical Sciences Ser.: Mathematical Theory of Incompressible...

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Item specifics

Condition
Very Good: A book that does not look new and has been read but is in excellent condition. No obvious ...
ISBN
9780387940441
Subject Area
Mathematics, Science
Publication Name
Mathematical Theory of Incompressible Nonviscous Fluids
Publisher
Springer New York
Item Length
9.2 in
Subject
Mechanics / Fluids, Differential Equations / General, Mathematical Analysis
Publication Year
1993
Series
Applied Mathematical Sciences Ser.
Type
Textbook
Format
Hardcover
Language
English
Author
Carlo Marchioro, Mario Pulvirenti
Item Weight
46.6 Oz
Item Width
6.1 in
Number of Pages
Xii, 284 Pages
Category

About this product

Product Identifiers

Publisher
Springer New York
ISBN-10
0387940448
ISBN-13
9780387940441
eBay Product ID (ePID)
973980

Product Key Features

Number of Pages
Xii, 284 Pages
Language
English
Publication Name
Mathematical Theory of Incompressible Nonviscous Fluids
Publication Year
1993
Subject
Mechanics / Fluids, Differential Equations / General, Mathematical Analysis
Type
Textbook
Subject Area
Mathematics, Science
Author
Carlo Marchioro, Mario Pulvirenti
Series
Applied Mathematical Sciences Ser.
Format
Hardcover

Dimensions

Item Weight
46.6 Oz
Item Length
9.2 in
Item Width
6.1 in

Additional Product Features

Intended Audience
Scholarly & Professional
LCCN
93-004683
Series Volume Number
96
Number of Volumes
1 vol.
Illustrated
Yes
Table Of Content
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.
Synopsis
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., 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.
LC Classification Number
QA299.6-433

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