Initial-Boundary Value Problems and the Navier-Stokes Equations
Academic Press
Published on 1. June 1989
406 pages
978-0-08-087456-2 (ISBN)
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Initial-Boundary Value Problems and the Navier-Stokes Equations
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Heinz-Otto Kreis | Jens Lorenz
Initial Boundary Value Problems and the Navier-Stokes Equations
Book
11/1997
Academic Press
€86.80
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Content
- Front Cover
- Initial-Boundary Value Problems and the Navier-Stokes Equations
- Copyright Page
- Contents
- Introduction
- Chapter 1. The Navier-Stokes Equations
- 1.1 Some Aspects of Our Approach
- 1.2 Derivation of the Navier-Stokes Equations
- 1.3 Linearization and Localization
- Chapter 2. Constant-Coefficient Cauchy Problems
- 2.1 Pure Exponentials as Initial Data
- 2.2 Discussion of Concepts of Well-Posedness
- 2.3 Algebraic Characterization of Well-Posedness
- 2.4 Hyperbolic and Parabolic Systems
- 2.5 Mixed Systems and the Compressible N-S Equations Linearized at Constant Flow
- 2.6 Properties of Constant-Coefficient Equations
- 2.7 The Spatially Periodic Cauchy Problem: A Summary for Variable Coefficients
- Notes on Chapter 2
- Chapter 3. Linear Variable-Coefficient Cauchy Problems in 1D
- 3.1 A Priori Estimates for Strongly Parabolic Problems
- 3.2 Existence for Parabolic Problems via Difference Approximations
- 3.3 Hyperbolic Systems: Existence and Properties of Solutions
- 3.4 Mixed Hyperbolic-Parabolic Systems
- 3.5 The Linearized Navier-Stokes Equations in One Space Dimension
- 3.6. The Linearized KdV and the Schrodinger Equations
- Notes on Chapter 3
- Chapter 4. A Nonlinear Example: Burgers' Equation
- 4.1 Burgers' Equation: A Priori Estimates and Local Existence
- 4.2 Global Existence for the Viscous Burgers' Equation
- 4.3 Generalized Solutions for Burgers' Equation and Smoothing
- 4.4 The Inviscid Burgers' Equation: A First Study of Shocks
- Notes on Chapter 4
- Chapter 5. Nonlinear Systems in One Space Dimension
- 5.1 The Case of Bounded Coefficients
- 5.2 Local Existence Theorems
- 5.3 Finite Time Existence and Asymptotic Expansions
- 5.4 On Global Existence for Parabolic and Mixed Systems
- Notes on Chapter 5
- Chapter 6. The Cauchy Problem for Systems in Several Dimensions
- 6.1 Linear Parabolic Systems
- 6.2 Linear Hyperbolic Systems
- 6.3 Mixed Hyperbolic-Parabolic Systems and the Linearized Navier-Stokes Equations
- 6.4 Short-Time Existence for Nonlinear Systems
- 6.5 A Global Existence Theorem in 2D
- Notes on Chapter 6
- Chapter 7. Initial-Boundary Value Problems in One Space Dimension
- 7.1 A Strip Problem for the Heat Equation
- 7.2 Strip Problems for Strongly Parabolic Systems
- 7.3 Discussion of Concepts of Well-Posedness
- 7.4 Half-Space Problems and the Laplace Transform
- 7.5 Mildly 111-Posed Half-Space Problems
- 7.6 Initial-Boundary Value Problems for Hyperbolic Equations
- 7.7 Boundary Conditions for Hyperbolic-Parabolic Problems
- 7.8 Semibounded Operators
- Notes on Chapter 7
- Chapter 8. Initial-Boundary Value Problems in Several Space Dimensions
- 8.1 Linear Strongly Parabolic Systems
- 8.2 Symmetric Hyperbolic Systems in Several Space Dimensions
- 8.3 The Linearized Compressible Euler Equations
- 8.4 The Laplace Transform Method for Hyperbolic Systems
- 8.5 Remarks on Mixed Systems and Nonlinear Problems
- Notes on Chapter 8
- Chapter 9. The Incompressible Navier-Stokes Equations: The Spatially Periodic Case
- 9.1 The Spatially Periodic Case in Two Dimensions
- 9.2 The Spatially Periodic Case in Three Dimensions
- Chapter 10. The Incompressible Navier-Stokes Equations under Initial and Boundary Conditions
- 10.1 The Linearized Equations in 2D
- 10.2 Auxiliary Results for Poisson's Equation
- 10.3 The Linearized Navier-Stokes Equations under Boundary Conditions
- 10.4 Remarks on the Passage from the Compressible to the Incompressible Equations
- Appendix 1: Notations and Results from Linear Algebra
- Appendix 2: Interpolation
- Appendix 3: Sobolev Inequalities
- Appendix 4: Application of the Arzela-Ascoil Theorem
- References
- Author Index
- Subject Index
