UID:
almafu_9958057471602883
Format:
1 online resource (421 p.)
ISBN:
1-281-76655-0
,
9786611766559
,
0-08-087456-8
Series Statement:
Pure and applied mathematics ; v. 136
Content:
Initial-boundary value problems and the Navier-Stokes equations
Note:
Description based upon print version of record.
,
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
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2.6 Properties of Constant-Coefficient Equations2.7 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
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Chapter 4. A Nonlinear Example: Burgers' Equation4.1 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
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Chapter 6. The Cauchy Problem for Systems in Several Dimensions6.1 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
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7.5 Mildly 111-Posed Half-Space Problems7.6 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
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Chapter 9. The Incompressible Navier-Stokes Equations: The Spatially Periodic Case
,
English
Additional Edition:
ISBN 0-12-426125-6
Language:
English
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