Description |
1 online resource (778 p.) |
Contents |
Intro -- Cover Page -- Half-Title Page -- Title Page -- Copyright Page -- Contents -- Preface to the First Edition -- Preface to the Second Edition -- 1 Presentation of the Clay Millennium Prizes -- 1.1 Regularity of the Three-Dimensional Fluid Flows: A Mathematical Challenge for the 21st Century -- 1.2 The Clay Millennium Prizes -- 1.3 The Clay Millennium Prize for the Navier-Stokes Equations -- 1.4 Boundaries and the Navier-Stokes Clay Millennium Problem -- 2 The Physical Meaning of the Navier-Stokes Equations -- 2.1 Frames of References -- 2.2 The Convection Theorem |
|
2.3 Conservation of Mass -- 2.4 Newton's Second Law -- 2.5 Pressure -- 2.6 Strain -- 2.7 Stress -- 2.8 The Equations of Hydrodynamics -- 2.9 The Navier-Stokes Equations -- 2.10 Vorticity -- 2.11 Boundary Terms -- 2.12 Blow-up -- 2.13 Turbulence -- 3 History of the Equation -- 3.1 Mechanics in the Scientific Revolution Era -- 3.2 Bernoulli's Hydrodymica -- 3.3 D'Alembert -- 3.4 Euler -- 3.5 Laplacian Physics -- 3.6 Navier, Cauchy, Poisson, Saint-Venant and Stokes -- 3.7 Reynolds -- 3.8 Oseen, Leray, Hopf and Ladyzhenskaya -- 3.9 Turbulence Models -- 4 Classical Solutions -- 4.1 The Heat Kernel |
|
4.2 The Poisson Equation -- 4.3 The Helmholtz Decomposition -- 4.4 The Stokes Equation -- 4.5 The Oseen Tensor -- 4.6 Classical Solutions for the Navier-Stokes Problem -- 4.7 Maximal Classical Solutions and Estimates in L∞ Norms -- 4.8 Small Data -- 4.9 Spatial Asymptotics -- 4.10 Spatial Asymptotics for the Vorticity -- 4.11 Maximal Classical Solutions and Estimates in L2 Norms -- 4.12 Intermediate Conclusion -- 5 A Capacitary Approach of the Navier-Stokes Integral Equations -- 5.1 The Integral Navier-Stokes Problem -- 5.2 Quadratic Equations in Banach Spaces |
|
5.3 A Capacitary Approach of Quadratic Integral Equations -- 5.4 Generalized Riesz Potentials on Spaces of Homogeneous Type -- 5.5 Dominating Functions for the Navier-Stokes Integral Equations -- 5.6 Oseen's Theorem and Dominating Functions -- 5.7 Functional Spaces and Multipliers -- 6 The Differential and the Integral Navier-Stokes Equations -- 6.1 Very Weak Solutions for the Navier-Stokes Equations -- 6.2 Heat Equation -- 6.3 The Leray Projection Operator -- 6.4 Stokes Equations -- 6.5 Oseen Equations -- 6.6 Mild Solutions for the Navier-Stokes Equations |
|
6.7 Suitable Solutions for the Navier-Stokes Equations -- 7 Mild Solutions in Lebesgue or Sobolev Spaces -- 7.1 Kato's Mild Solutions -- 7.2 Local Solutions in the Hilbertian Setting -- 7.3 Global Solutions in the Hilbertian Setting -- 7.4 Sobolev Spaces -- 7.5 A Commutator Estimate -- 7.6 Lebesgue Spaces -- 7.7 Maximal Functions -- 7.8 Basic Lemmas on Real Interpolation Spaces -- 7.9 Uniqueness of L3 Solutions -- 8 Mild Solutions in Besov or Morrey Spaces -- 8.1 Morrey Spaces -- 8.2 Morrey Spaces and Maximal Functions -- 8.3 Uniqueness of Morrey Solutions -- 8.4 Besov Spaces |
Summary |
This book provides a self-contained guide to the role of harmonic analysis in the PDEs of fluid mechanics, now revised to include fresh examples, theorems, results, and references that have become relevant since the first edition published in 2016 |
Notes |
Description based upon print version of record |
|
8.5 Regular Besov Spaces |
Form |
Electronic book
|
ISBN |
9781003807445 |
|
1003807445 |
|