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Tables of Contents for Navier-Stokes Equations
Chapter/Section Title
Page #
Page Count
Preface to the AMS Chelsea edition
ix
 
Preface to the third (revised) edition
xi
 
Foreword
xiii
 
The Steady-State Stokes Equations
1
104
Introduction
1
1
Some function spaces
1
14
Existence and uniqueness for the Stokes equations
15
13
Discretization of the Stokes equations (I)
28
17
Discretization of Stokes Equations (II)
45
46
Numerical algorithms
91
7
The penalty method
98
7
Steady-State Navier-Stokes Equations
105
62
Introduction
105
1
Existence and uniqueness theorems
105
16
Discrete inequalities and compactness theorems
121
13
Approximation of the stationary Navier-Stokes equations
134
16
Bifurcation theory and non-uniqueness results
150
17
The Evolution Navier-Stokes Equation
167
144
Introduction
167
1
The linear case
167
15
Compactness theorems
182
7
Existence and uniqueness theorems (n ≤ 4)
189
27
Alternate proof of existence by semi-discretization
216
8
Discretization of the Navier-Stokes equations: General stability and convergence theorems
224
22
Discretization of the Navier-Stokes equations: Application of the general results
246
21
Approximation of the Navier-Stokes equations by the projection method
267
20
Approximation of the Navier-Stokes equations by the artificial compressibility method
287
24
Appendix I. Properties of the Curl Operator and Application to the Steady-State Navier-Stokes Equations
311
10
1. Functional properties of the curl operator
311
7
2. Application to the non-homogeneous steady-state Navier-Stokes equations
318
3
Appendix II. Implementation of Non-conforming Linear Finite Elements (Approximation APX5-Two-dimensional Case)
321
16
F. Thomasset
0. Test problems
321
1
1. The triangulation
321
5
2. The nodes
326
1
3. Computation of the basis function on a given triangle
327
2
4. Solution of the Stokes problem
329
4
5. Solution of Navier-Stokes equations
333
4
Appendix III. Some Development on Navier-Stokes Equations in the Second Half of the 20th Century
337
44
Introduction
337
2
Part I: The incompressible Navier-Stokes equations
339
1
1. Existence, uniqueness and regularity of solutions
339
14
2. Attractors and turbulence
348
5
Part II: Other problems, other equations
353
1
3. Compressible and inviscid flows
353
5
4. Some other problems and equations
358
23
Bibliography to Appendix III
363
18
Comments
381
6
Chapter 1
381
1
Chapter 2
382
1
Chapter 3
383
4
Additional comments to the third (revised) edition
387
2
Bibliography (to the core of the book)
389
18
Index
407