Contributions to current challenges in mathematical fluid mechanics

✍ Scribed by Giovanni P. Galdi, John G. Heywood, Rolf Rannacher

• Publisher: Birkhauser
• Year: 2004
• Tongue: English
• Leaves: 162
• Series: Advances in Mathematical Fluid Mechanics
• Category: Library

✦ Synopsis

The mathematical theory of the Navier-Stokes equations presents still fundamental open questions that represent as many challenges for the interested mathematicians. This volume collects a series of articles whose objective is to furnish new contributions and ideas to these questions, with particular regard to turbulence modelling, regularity of solutions to the initial-value problem, flow in region with an unbounded boundary and compressible flow.

✦ Table of Contents

Cover......Page 1
Title Page......Page 4
Copyright......Page 5
Contents......Page 6
Preface......Page 8
1. Introduction......Page 10
2. Upper estimates......Page 13
3. Lower estimates......Page 16
4. Fourier coefficients......Page 26
5. Low bounds for spatial derivatives of solutions of the Navier Stokes system......Page 36
References......Page 38
1. Introduction......Page 40
2. Littlewood-Paley decomposition......Page 42
3. Proof of Theorems......Page 45
Appendix......Page 56
References......Page 58
1. Introduction......Page 62
2. The space averaged Navier-Stokes equations in a bounded domain......Page 64
3. The Gaussian filter......Page 67
4. Error estimates in the (L^P(R^d))d-norm of the commutation error term......Page 68
5. Error estimates in the (H-I (ft))`r norm of the commutation error term......Page 75
6. Error estimates for a weak form of the commutation error term......Page 77
7. The boundedness of the kinetic energy for u in some LES models......Page 81
References......Page 85
1. Introduction......Page 88
2. Results......Page 94
3. The Stokes resolvent for the half space......Page 99
4. The Stokes resolvent......Page 105
5. LQ-L' estimates of the Stokes semigroup......Page 112
6. The Navier-Stokes flow......Page 121
References......Page 129
1. Introduction......Page 134
2. Function spaces and auxiliary results......Page 138
3. Stokes and modified Stokes problems in weighted spaces......Page 141
4. Transport equation and Poisson-type equation......Page 149
5. Linearized problem......Page 152
6. Nonlinear problem......Page 156
References......Page 159