The Resource Vorticity and incompressible flow, Andrew J. Majda, Andrea L. Bertozzi
Vorticity and incompressible flow, Andrew J. Majda, Andrea L. Bertozzi
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The item Vorticity and incompressible flow, Andrew J. Majda, Andrea L. Bertozzi represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Missouri University of Science & Technology Library.This item is available to borrow from 1 library branch.
Resource Information
The item Vorticity and incompressible flow, Andrew J. Majda, Andrea L. Bertozzi represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Missouri University of Science & Technology Library.
This item is available to borrow from 1 library branch.
 Extent
 xii, 545 pages
 Contents

 1. An Introduction to Vortex Dynamics for Incompressible Fluid Flows. 1.1. The Euler and the NavierStokes Equations. 1.2. Symmetry Groups for the Euler and the NavierStokes Equations. 1.3. Particle Trajectories. 1.4. The Vorticity, a Deformation Matrix, and Some Elementary Exact Solutions. 1.5. Simple Exact Solutions with Convection, Vortex Stretching, and Diffusion. 1.6. Some Remarkable Properties of the Vorticity in Ideal Fluid Flows. 1.7. Conserved Quantities in Ideal and Viscous Fluid Flows. 1.8. Leray's Formulation of Incompressible Flows and Hodge's Decomposition of Vector Fields
 2. The VorticityStream Formulation of the Euler and the NavierStokes Equations. 2.1. The VorticityStream Formulation for 2D Flows. 2.2. A General Method for Constructing Exact Steady Solutions to the 2D Euler Equations. 2.3. Some Special 3D Flows with Nontrivial Vortex Dynamics. 2.4. The VorticityStream Formulation for 3D Flows. 2.5. Formulation of the Euler Equation as an Integrodifferential Equation for the Particle Trajectories
 3. Energy Methods for the Euler and the NavierStokes Equations. 3.1. Energy Methods: Elementary Concepts. 3.2. LocalinTime Existence of Solutions by Means of Energy Methods. 3.3. Accumulation of Vorticity and the Existence of Smooth Solutions Globally in Time. 3.4. ViscousSplitting Algorithms for the NavierStokes Equation
 4. The ParticleTrajectory Method for Existence and Uniqueness of Solutions to the Euler Equation. 4.1. The LocalinTime Existence of Inviscid Solutions. 4.2. Link between GlobalinTime Existence of Smooth Solutions and the Accumulation of Vorticity through Stretching. 4.3. Global Existence of 3D Axisymmetric Flows without Swirl. 4.4. Higher Regularity
 5. The Search for Singular Solutions to the 3D Euler Equations. 5.1. The Interplay between Mathematical Theory and Numerical Computations in the Search for Singular Solutions. 5.2. A Simple 1D Model for the 3D Vorticity Equation. 5.3. A 2D Model for Potential Singularity Formation in 3D Euler Equations. 5.4. Potential Singularities in 3D Axisymmetric Flows with Swirl. 5.5. Do the 2D Euler Solutions Become Singular in Finite Times?
 6. Computational Vortex Methods. 6.1. The RandomVortex Method for Viscous Strained Shear Layers. 6.2. 2D Inviscid Vortex Methods. 6.3. 3D InviscidVortex Methods. 6.4. Convergence of InviscidVortex Methods. 6.5. Computational Performance of the 2D InviscidVortex Method on a Simple Model Problem. 6.6. The RandomVortex Method in Two Dimensions
 7. Simplified Asymptotic Equations for Slender Vortex Filaments. 7.1. The SelfInduction Approximation, Hasimoto's Transform, and the Nonlinear Schrodinger Equation. 7.2. Simplified Asymptotic Equations with SelfStretch for a Single Vortex Filament. 7.3. Interacting Parallel Vortex Filaments  Point Vortices in the Plane. 7.4. Asymptotic Equations for the Interaction of Nearly Parallel Vortex Filaments. 7.5. Mathematical and Applied Mathematical Problems Regarding Asymptotic Vortex Filaments
 8. Weak Solutions to the 2D Euler Equations with Initial Vorticity in L[superscript [infinity]]. 8.1. Elliptical Vorticies. 8.2. Weak L[superscript [infinity]] Solutions to the Vorticity Equation. 8.3. Vortex Patches
 9. Introduction to Vortex Sheets, Weak Solutions, and ApproximateSolution Sequences for the Euler Equation. 9.1. Weak Formulation of the Euler Equation in PrimitiveVariable Form. 9.2. Classical Vortex Sheets and the BirkhoffRott Equation. 9.3. The KelvinHelmholtz Instability. 9.4. Computing Vortex Sheets. 9.5. The Development of Oscillations and Concentrations
 10. Weak Solutions and Solution Sequences in Two Dimensions. 10.1. ApproximateSolution Sequences for the Euler and the NavierStokes Equations. 10.2. Convergence Results for 2D Sequences with L[superscript l] and L[superscript p] Vorticity Control
 11. The 2D Euler Equation: Concentrations and Weak Solutions with VortexSheet Initial Data. 11.1. Weak and Reduced Defect Measures. 11.2. Examples with Concentration. 11.3. The Vorticity Maximal Function: Decay Rates and Strong Convergence. 11.4. Existence of Weak Solutions with VortexSheet Initial Data of Distinguished Sign
 12. Reduced Hausdorff Dimension, Oscillations, and MeasureValued Solutions of the Euler Equations in Two and Three Dimensions. 12.1. The Reduced Hausdorff Dimension. 12.2. Oscillations for ApproximateSolution Sequences without L[superscript l] Vorticity Control. 12.3. Young Measures and MeasureValued Solutions of the Euler Equations. 12.4. MeasureValued Solutions with Oscillations and Concentrations
 13. The VlasovPoisson Equations as an Analogy to the Euler Equations for the Study of Weak Solutions. 13.1. The Analogy between the 2D Euler Equations and the 1D VlasovPoisson Equations. 13.2. The SingleComponent 1D VlasovPoisson Equation. 13.3. The TwoComponent 1D VlasovPoisson System
 Isbn
 9780521630573
 Label
 Vorticity and incompressible flow
 Title
 Vorticity and incompressible flow
 Statement of responsibility
 Andrew J. Majda, Andrea L. Bertozzi
 Language
 eng
 Cataloging source
 DLC
 http://library.link/vocab/creatorDate
 1949
 http://library.link/vocab/creatorName
 Majda, Andrew
 Dewey number
 532/.059
 Illustrations
 illustrations
 Index
 index present
 LC call number
 QA925
 LC item number
 .M35 2002
 Literary form
 non fiction
 Nature of contents
 bibliography
 http://library.link/vocab/relatedWorkOrContributorName
 Bertozzi, Andrea L
 Series statement
 Cambridge texts in applied mathematics
 http://library.link/vocab/subjectName

 Vortexmotion
 NonNewtonian fluids
 Label
 Vorticity and incompressible flow, Andrew J. Majda, Andrea L. Bertozzi
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 volume
 Carrier category code

 nc
 Carrier MARC source
 rdacarrier
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 1. An Introduction to Vortex Dynamics for Incompressible Fluid Flows. 1.1. The Euler and the NavierStokes Equations. 1.2. Symmetry Groups for the Euler and the NavierStokes Equations. 1.3. Particle Trajectories. 1.4. The Vorticity, a Deformation Matrix, and Some Elementary Exact Solutions. 1.5. Simple Exact Solutions with Convection, Vortex Stretching, and Diffusion. 1.6. Some Remarkable Properties of the Vorticity in Ideal Fluid Flows. 1.7. Conserved Quantities in Ideal and Viscous Fluid Flows. 1.8. Leray's Formulation of Incompressible Flows and Hodge's Decomposition of Vector Fields  2. The VorticityStream Formulation of the Euler and the NavierStokes Equations. 2.1. The VorticityStream Formulation for 2D Flows. 2.2. A General Method for Constructing Exact Steady Solutions to the 2D Euler Equations. 2.3. Some Special 3D Flows with Nontrivial Vortex Dynamics. 2.4. The VorticityStream Formulation for 3D Flows. 2.5. Formulation of the Euler Equation as an Integrodifferential Equation for the Particle Trajectories  3. Energy Methods for the Euler and the NavierStokes Equations. 3.1. Energy Methods: Elementary Concepts. 3.2. LocalinTime Existence of Solutions by Means of Energy Methods. 3.3. Accumulation of Vorticity and the Existence of Smooth Solutions Globally in Time. 3.4. ViscousSplitting Algorithms for the NavierStokes Equation  4. The ParticleTrajectory Method for Existence and Uniqueness of Solutions to the Euler Equation. 4.1. The LocalinTime Existence of Inviscid Solutions. 4.2. Link between GlobalinTime Existence of Smooth Solutions and the Accumulation of Vorticity through Stretching. 4.3. Global Existence of 3D Axisymmetric Flows without Swirl. 4.4. Higher Regularity  5. The Search for Singular Solutions to the 3D Euler Equations. 5.1. The Interplay between Mathematical Theory and Numerical Computations in the Search for Singular Solutions. 5.2. A Simple 1D Model for the 3D Vorticity Equation. 5.3. A 2D Model for Potential Singularity Formation in 3D Euler Equations. 5.4. Potential Singularities in 3D Axisymmetric Flows with Swirl. 5.5. Do the 2D Euler Solutions Become Singular in Finite Times?  6. Computational Vortex Methods. 6.1. The RandomVortex Method for Viscous Strained Shear Layers. 6.2. 2D Inviscid Vortex Methods. 6.3. 3D InviscidVortex Methods. 6.4. Convergence of InviscidVortex Methods. 6.5. Computational Performance of the 2D InviscidVortex Method on a Simple Model Problem. 6.6. The RandomVortex Method in Two Dimensions  7. Simplified Asymptotic Equations for Slender Vortex Filaments. 7.1. The SelfInduction Approximation, Hasimoto's Transform, and the Nonlinear Schrodinger Equation. 7.2. Simplified Asymptotic Equations with SelfStretch for a Single Vortex Filament. 7.3. Interacting Parallel Vortex Filaments  Point Vortices in the Plane. 7.4. Asymptotic Equations for the Interaction of Nearly Parallel Vortex Filaments. 7.5. Mathematical and Applied Mathematical Problems Regarding Asymptotic Vortex Filaments  8. Weak Solutions to the 2D Euler Equations with Initial Vorticity in L[superscript [infinity]]. 8.1. Elliptical Vorticies. 8.2. Weak L[superscript [infinity]] Solutions to the Vorticity Equation. 8.3. Vortex Patches  9. Introduction to Vortex Sheets, Weak Solutions, and ApproximateSolution Sequences for the Euler Equation. 9.1. Weak Formulation of the Euler Equation in PrimitiveVariable Form. 9.2. Classical Vortex Sheets and the BirkhoffRott Equation. 9.3. The KelvinHelmholtz Instability. 9.4. Computing Vortex Sheets. 9.5. The Development of Oscillations and Concentrations  10. Weak Solutions and Solution Sequences in Two Dimensions. 10.1. ApproximateSolution Sequences for the Euler and the NavierStokes Equations. 10.2. Convergence Results for 2D Sequences with L[superscript l] and L[superscript p] Vorticity Control  11. The 2D Euler Equation: Concentrations and Weak Solutions with VortexSheet Initial Data. 11.1. Weak and Reduced Defect Measures. 11.2. Examples with Concentration. 11.3. The Vorticity Maximal Function: Decay Rates and Strong Convergence. 11.4. Existence of Weak Solutions with VortexSheet Initial Data of Distinguished Sign  12. Reduced Hausdorff Dimension, Oscillations, and MeasureValued Solutions of the Euler Equations in Two and Three Dimensions. 12.1. The Reduced Hausdorff Dimension. 12.2. Oscillations for ApproximateSolution Sequences without L[superscript l] Vorticity Control. 12.3. Young Measures and MeasureValued Solutions of the Euler Equations. 12.4. MeasureValued Solutions with Oscillations and Concentrations  13. The VlasovPoisson Equations as an Analogy to the Euler Equations for the Study of Weak Solutions. 13.1. The Analogy between the 2D Euler Equations and the 1D VlasovPoisson Equations. 13.2. The SingleComponent 1D VlasovPoisson Equation. 13.3. The TwoComponent 1D VlasovPoisson System
 Control code
 45002202
 Dimensions
 26 cm
 Extent
 xii, 545 pages
 Isbn
 9780521630573
 Lccn
 00046776
 Media category
 unmediated
 Media MARC source
 rdamedia
 Media type code

 n
 Other physical details
 illustrations
 Label
 Vorticity and incompressible flow, Andrew J. Majda, Andrea L. Bertozzi
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 volume
 Carrier category code

 nc
 Carrier MARC source
 rdacarrier
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 1. An Introduction to Vortex Dynamics for Incompressible Fluid Flows. 1.1. The Euler and the NavierStokes Equations. 1.2. Symmetry Groups for the Euler and the NavierStokes Equations. 1.3. Particle Trajectories. 1.4. The Vorticity, a Deformation Matrix, and Some Elementary Exact Solutions. 1.5. Simple Exact Solutions with Convection, Vortex Stretching, and Diffusion. 1.6. Some Remarkable Properties of the Vorticity in Ideal Fluid Flows. 1.7. Conserved Quantities in Ideal and Viscous Fluid Flows. 1.8. Leray's Formulation of Incompressible Flows and Hodge's Decomposition of Vector Fields  2. The VorticityStream Formulation of the Euler and the NavierStokes Equations. 2.1. The VorticityStream Formulation for 2D Flows. 2.2. A General Method for Constructing Exact Steady Solutions to the 2D Euler Equations. 2.3. Some Special 3D Flows with Nontrivial Vortex Dynamics. 2.4. The VorticityStream Formulation for 3D Flows. 2.5. Formulation of the Euler Equation as an Integrodifferential Equation for the Particle Trajectories  3. Energy Methods for the Euler and the NavierStokes Equations. 3.1. Energy Methods: Elementary Concepts. 3.2. LocalinTime Existence of Solutions by Means of Energy Methods. 3.3. Accumulation of Vorticity and the Existence of Smooth Solutions Globally in Time. 3.4. ViscousSplitting Algorithms for the NavierStokes Equation  4. The ParticleTrajectory Method for Existence and Uniqueness of Solutions to the Euler Equation. 4.1. The LocalinTime Existence of Inviscid Solutions. 4.2. Link between GlobalinTime Existence of Smooth Solutions and the Accumulation of Vorticity through Stretching. 4.3. Global Existence of 3D Axisymmetric Flows without Swirl. 4.4. Higher Regularity  5. The Search for Singular Solutions to the 3D Euler Equations. 5.1. The Interplay between Mathematical Theory and Numerical Computations in the Search for Singular Solutions. 5.2. A Simple 1D Model for the 3D Vorticity Equation. 5.3. A 2D Model for Potential Singularity Formation in 3D Euler Equations. 5.4. Potential Singularities in 3D Axisymmetric Flows with Swirl. 5.5. Do the 2D Euler Solutions Become Singular in Finite Times?  6. Computational Vortex Methods. 6.1. The RandomVortex Method for Viscous Strained Shear Layers. 6.2. 2D Inviscid Vortex Methods. 6.3. 3D InviscidVortex Methods. 6.4. Convergence of InviscidVortex Methods. 6.5. Computational Performance of the 2D InviscidVortex Method on a Simple Model Problem. 6.6. The RandomVortex Method in Two Dimensions  7. Simplified Asymptotic Equations for Slender Vortex Filaments. 7.1. The SelfInduction Approximation, Hasimoto's Transform, and the Nonlinear Schrodinger Equation. 7.2. Simplified Asymptotic Equations with SelfStretch for a Single Vortex Filament. 7.3. Interacting Parallel Vortex Filaments  Point Vortices in the Plane. 7.4. Asymptotic Equations for the Interaction of Nearly Parallel Vortex Filaments. 7.5. Mathematical and Applied Mathematical Problems Regarding Asymptotic Vortex Filaments  8. Weak Solutions to the 2D Euler Equations with Initial Vorticity in L[superscript [infinity]]. 8.1. Elliptical Vorticies. 8.2. Weak L[superscript [infinity]] Solutions to the Vorticity Equation. 8.3. Vortex Patches  9. Introduction to Vortex Sheets, Weak Solutions, and ApproximateSolution Sequences for the Euler Equation. 9.1. Weak Formulation of the Euler Equation in PrimitiveVariable Form. 9.2. Classical Vortex Sheets and the BirkhoffRott Equation. 9.3. The KelvinHelmholtz Instability. 9.4. Computing Vortex Sheets. 9.5. The Development of Oscillations and Concentrations  10. Weak Solutions and Solution Sequences in Two Dimensions. 10.1. ApproximateSolution Sequences for the Euler and the NavierStokes Equations. 10.2. Convergence Results for 2D Sequences with L[superscript l] and L[superscript p] Vorticity Control  11. The 2D Euler Equation: Concentrations and Weak Solutions with VortexSheet Initial Data. 11.1. Weak and Reduced Defect Measures. 11.2. Examples with Concentration. 11.3. The Vorticity Maximal Function: Decay Rates and Strong Convergence. 11.4. Existence of Weak Solutions with VortexSheet Initial Data of Distinguished Sign  12. Reduced Hausdorff Dimension, Oscillations, and MeasureValued Solutions of the Euler Equations in Two and Three Dimensions. 12.1. The Reduced Hausdorff Dimension. 12.2. Oscillations for ApproximateSolution Sequences without L[superscript l] Vorticity Control. 12.3. Young Measures and MeasureValued Solutions of the Euler Equations. 12.4. MeasureValued Solutions with Oscillations and Concentrations  13. The VlasovPoisson Equations as an Analogy to the Euler Equations for the Study of Weak Solutions. 13.1. The Analogy between the 2D Euler Equations and the 1D VlasovPoisson Equations. 13.2. The SingleComponent 1D VlasovPoisson Equation. 13.3. The TwoComponent 1D VlasovPoisson System
 Control code
 45002202
 Dimensions
 26 cm
 Extent
 xii, 545 pages
 Isbn
 9780521630573
 Lccn
 00046776
 Media category
 unmediated
 Media MARC source
 rdamedia
 Media type code

 n
 Other physical details
 illustrations
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