Book contents
- Frontmatter
- Contents
- Preface
- 1 An Introduction to Vortex Dynamics for Incompressible Fluid Flows
- 2 The Vorticity-Stream Formulation of the Euler and the Navier-Stokes Equations
- 3 Energy Methods for the Euler and the Navier–Stokes Equations
- 4 The Particle-Trajectory Method for Existence and Uniqueness of Solutions to the Euler Equation
- 5 The Search for Singular Solutions to the 3D Euler Equations
- 6 Computational Vortex Methods
- 7 Simplified Asymptotic Equations for Slender Vortex Filaments
- 8 Weak Solutions to the 2D Euler Equations with Initial Vorticity in L∞
- 9 Introduction to Vortex Sheets, Weak Solutions, and Approximate-Solution Sequences for the Euler Equation
- 10 Weak Solutions and Solution Sequences in Two Dimensions
- 11 The 2D Euler Equation: Concentrations and Weak Solutions with Vortex-Sheet Initial Data
- 12 Reduced Hausdorff Dimension, Oscillations, and Measure-Valued Solutions of the Euler Equations in Two and Three Dimensions
- 13 The Vlasov–Poisson Equations as an Analogy to the Euler Equations for the Study of Weak Solutions
- Index
9 - Introduction to Vortex Sheets, Weak Solutions, and Approximate-Solution Sequences for the Euler Equation
Published online by Cambridge University Press: 03 February 2010
Book contents
- Frontmatter
- Contents
- Preface
- 1 An Introduction to Vortex Dynamics for Incompressible Fluid Flows
- 2 The Vorticity-Stream Formulation of the Euler and the Navier-Stokes Equations
- 3 Energy Methods for the Euler and the Navier–Stokes Equations
- 4 The Particle-Trajectory Method for Existence and Uniqueness of Solutions to the Euler Equation
- 5 The Search for Singular Solutions to the 3D Euler Equations
- 6 Computational Vortex Methods
- 7 Simplified Asymptotic Equations for Slender Vortex Filaments
- 8 Weak Solutions to the 2D Euler Equations with Initial Vorticity in L∞
- 9 Introduction to Vortex Sheets, Weak Solutions, and Approximate-Solution Sequences for the Euler Equation
- 10 Weak Solutions and Solution Sequences in Two Dimensions
- 11 The 2D Euler Equation: Concentrations and Weak Solutions with Vortex-Sheet Initial Data
- 12 Reduced Hausdorff Dimension, Oscillations, and Measure-Valued Solutions of the Euler Equations in Two and Three Dimensions
- 13 The Vlasov–Poisson Equations as an Analogy to the Euler Equations for the Study of Weak Solutions
- Index
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- Vorticity and Incompressible Flow , pp. 359 - 382Publisher: Cambridge University PressPrint publication year: 2001