Vorticity and incompressible flow:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
Cambridge
Cambridge Univ. Press
2002
|
| Series: | Cambridge texts in applied mathematics
27 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XII, 545 S. graph. Darst. |
| ISBN: | 0521630576 9780521630573 9780521639484 |
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MARC
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| 245 | 1 | 0 | |a Vorticity and incompressible flow |c Andrew J. Majda ; Andrea L. Bertozzi |
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| 490 | 1 | |a Cambridge texts in applied mathematics |v 27 | |
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Record in the Search Index
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| adam_text | Contents
Preface page xi
1 An Introduction to Vortex Dynamics for Incompressible
Fluid Flows 1
1.1 The Euler and the Navier Stokes Equations 2
1.2 Symmetry Groups for the Euler and the Navier Stokes Equations 3
1.3 Particle Trajectories 4
1.4 The Vorticity, a Deformation Matrix, and Some Elementary
Exact Solutions 6
1.5 Simple Exact Solutions with Convection, Vortex Stretching,
and Diffusion 13
1.6 Some Remarkable Properties of the Vorticity in Ideal Fluid Flows 20
1.7 Conserved Quantities in Ideal and Viscous Fluid Flows 24
1.8 Leray s Formulation of Incompressible Flows and
Hodge s Decomposition of Vector Fields 30
1.9 Appendix 35
Notes for Chapter 1 41
References for Chapter 1 42
2 The Vorticity Stream Formulation of the Euler and
the Navier Stokes Equations 43
2.1 The Vorticity Stream Formulation for 2D Hows 44
2.2 A General Method for Constructing Exact Steady Solutions
to the 2D Euler Equations 46
2.3 Some Special 3D Flows with Nontrivial Vortex Dynamics 54
2.4 The Vorticity Stream Formulation for 3D Flows 70
2.5 Formulation of the Euler Equation as an Integrodifferential Equation
for the Particle Trajectories 81
Notes for Chapter 2 84
References for Chapter 2 84
3 Energy Methods for the Euler and the Navier Stokes Equations 86
3.1 Energy Methods: Elementary Concepts 87
vii
viii Contents
3.2 Local in Time Existence of Solutions by Means of Energy Methods 96
3.3 Accumulation of Vorticity and the Existence of Smooth Solutions
Globally in Time 114
3.4 Viscous Splitting Algorithms for the Navier Stokes Equation 119
3.5 Appendix for Chapter 3 129
Notes for Chapter 3 133
References for Chapter 3 134
4 The Particle Trajectory Method for Existence and Uniqueness
of Solutions to the Euler Equation 136
4.1 The Local in Time Existence of Inviscid Solutions 138
4.2 Link between Global in Time Existence of Smooth Solutions
and the Accumulation of Vorticity through Stretching 146
4.3 Global Existence of 3D Axisymmetric Flows without Swirl 152
4.4 Higher Regularity 155
4.5 Appendixes for Chapter 4 158
Notes for Chapter 4 166
References for Chapter 4 167
5 The Search for Singular Solutions to the 3D Euler Equations 168
5.1 The Interplay between Mathematical Theory and Numerical
Computations in the Search for Singular Solutions 170
5.2 A Simple ID Model for the 3D Vorticity Equation 173
5.3 A 2D Model for Potential Singularity Formation in 3D Euler Equations 177
5.4 Potential Singularities in 3D Axisymmetric Flows with Swirl 185
5.5 Do the 3D Euler Solutions Become Singular in Finite Times? 187
Notes for Chapter 5 188
References for Chapter 5 188
6 Computational Vortex Methods 190
6.1 The Random Vortex Method for Viscous Strained Shear Layers 192
6.2 2D Inviscid Vortex Methods 208
6.3 3D Inviscid Vortex Methods 211
6.4 Convergence of Inviscid Vortex Methods 216
6.5 Computational Performance of the 2D Inviscid Vortex Method
on a Simple Model Problem 227
6.6 The Random Vortex Method in Two Dimensions 232
6.7 Appendix for Chapter 6 247
Notes for Chapter 6 253
References for Chapter 6 254
7 Simplified Asymptotic Equations for Slender Vortex Filaments 256
7.1 The Self induction Approximation, Hasimoto s Transform,
and the Nonlinear Schrodinger Equation 257
Contents ix
7.2 Simplified Asymptotic Equations with Self Stretch
for a Single Vortex Filament 262
7.3 Interacting Parallel Vortex Filaments Point Vortices in the Plane 278
7.4 Asymptotic Equations for the Interaction of Nearly Parallel
Vortex Filaments 281
7.5 Mathematical and Applied Mathematical Problems Regarding
Asymptotic Vortex Filaments 300
Notes for Chapter 7 301
References for Chapter 7 301
8 Weak Solutions to the 2D Euler Equations with Initial Vorticity
inZ °° 303
8.1 Elliptical Vorticies 304
8.2 Weak L°° Solutions to the Vorticity Equation 309
8.3 Vortex Patches 329
8.4 Appendix for Chapter 8 354
Notes for Chapter 8 356
References for Chapter 8 356
9 Introduction to Vortex Sheets, Weak Solutions,
and Approximate Solution Sequences for the Euler Equation 359
9.1 Weak Formulation of the Euler Equation in Primitive Variable Form 361
9.2 Classical Vortex Sheets and the Birkhoff Rott Equation 363
9.3 The Kelvin Helmholtz Instability 367
9.4 Computing Vortex Sheets 370
9.5 The Development of Oscillations and Concentrations 375
Notes for Chapter 9 380
References for Chapter 9 380
10 Weak Solutions and Solution Sequences in Two Dimensions 383
10.1 Approximate Solution Sequences for the Euler and
the Navier Stokes Equations 385
10.2 Convergence Results for 2D Sequences with L1 and Lp
Vorticity Control 396
Notes for Chapter 10 403
References for Chapter 10 403
11 The 2D Euler Equation: Concentrations and Weak Solutions
with Vortex Sheet Initial Data 405
11.1 Weak * and Reduced Defect Measures 409
11.2 Examples with Concentration 411
11.3 The Vorticity Maximal Function: Decay Rates and Strong Convergence 421
11.4 Existence of Weak Solutions with Vortex Sheet Initial Data
of Distinguished Sign 432
Notes for Chapter 11 448
References for Chapter 11 448
x Contents
12 Reduced Hausdorff Dimension, Oscillations, and Measure Valued
Solutions of the Elder Equations in Two and Three Dimensions 450
12.1 The Reduced Hausdorff Dimension 452
12.2 OscDlations for Approximate Solution Sequences without L
Vorticity Control 472
12.3 Young Measures and Measure Valued Solutions of the Euler Equations 479
12.4 Measure Valued Solutions with Oscillations and Concentrations 492
Notes for Chapter 12 496
References for Chapter 12 496
13 The Vlasov Poisson Equations as an Analogy to the Euler
Equations for the Study of Weak Solutions 498
13.1 The Analogy between the 2D Euler Equations and
the ID Vlasov Poisson Equations 502
13.2 The Single Component ID Vlasov Poisson Equation 511
13.3 The Two Component Vlasov Poisson System 524
Note for Chapter 13 541
References for Chapter 13 541
Index 543
|
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| spelling | Majda, Andrew 1949- Verfasser (DE-588)135598788 aut Vorticity and incompressible flow Andrew J. Majda ; Andrea L. Bertozzi Cambridge Cambridge Univ. Press 2002 XII, 545 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Cambridge texts in applied mathematics 27 Hier auch später erschienene, unveränderte Nachdrucke Euler, équations d' ram Fluides non newtoniens Fluides non newtoniens ram Tourbillons (Mécanique des fluides) Tourbillons (mécanique des fluides) ram Non-Newtonian fluids Vortex-motion Inkompressible Strömung (DE-588)4129759-3 gnd rswk-swf Wirbelströmung (DE-588)4190007-8 gnd rswk-swf Wirbelströmung (DE-588)4190007-8 s Inkompressible Strömung (DE-588)4129759-3 s DE-604 Bertozzi, Andrea L. Verfasser aut Cambridge texts in applied mathematics 27 (DE-604)BV005466119 27 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017474254&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Majda, Andrew 1949- Bertozzi, Andrea L. Vorticity and incompressible flow Cambridge texts in applied mathematics Euler, équations d' ram Fluides non newtoniens Fluides non newtoniens ram Tourbillons (Mécanique des fluides) Tourbillons (mécanique des fluides) ram Non-Newtonian fluids Vortex-motion Inkompressible Strömung (DE-588)4129759-3 gnd Wirbelströmung (DE-588)4190007-8 gnd |
| subject_GND | (DE-588)4129759-3 (DE-588)4190007-8 |
| title | Vorticity and incompressible flow |
| title_auth | Vorticity and incompressible flow |
| title_exact_search | Vorticity and incompressible flow |
| title_full | Vorticity and incompressible flow Andrew J. Majda ; Andrea L. Bertozzi |
| title_fullStr | Vorticity and incompressible flow Andrew J. Majda ; Andrea L. Bertozzi |
| title_full_unstemmed | Vorticity and incompressible flow Andrew J. Majda ; Andrea L. Bertozzi |
| title_short | Vorticity and incompressible flow |
| title_sort | vorticity and incompressible flow |
| topic | Euler, équations d' ram Fluides non newtoniens Fluides non newtoniens ram Tourbillons (Mécanique des fluides) Tourbillons (mécanique des fluides) ram Non-Newtonian fluids Vortex-motion Inkompressible Strömung (DE-588)4129759-3 gnd Wirbelströmung (DE-588)4190007-8 gnd |
| topic_facet | Euler, équations d' Fluides non newtoniens Tourbillons (Mécanique des fluides) Tourbillons (mécanique des fluides) Non-Newtonian fluids Vortex-motion Inkompressible Strömung Wirbelströmung |
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