This book revises and expands upon the prior edition, The Navier-Stokes Problem. The focus of this book is to provide a mathematical analysis of the Navier-Stokes Problem (NSP) in R^3 without boundaries. Before delving into analysis, the author begins by explaining the background and history of the Navier-Stokes Problem. This edition includes new analysis and an a priori estimate of the solution. The estimate proves the contradictory nature of the Navier-Stokes Problem. The author reaches the conclusion that the solution to the NSP with smooth and rapidly decaying data cannot exist for all positive times. By proving the NSP paradox, this book provides a solution to the millennium problem concerning the Navier-Stokes Equations and shows that they are physically and mathematically contradictive.
Author(s): Alexander G. Ramm
Series: Synthesis Lectures on Mathematics & Statistics
Edition: 2
Publisher: Springer
Year: 2023
Language: English
Pages: 103
City: Cham
Preface to the Second Edition
Preface to the First Edition
Contents
About the Author
1 Introduction
2 Brief History of the Navier–Stokes Problem
3 Statement of the Navier–Stokes Problem
4 Theory of Some Hyper-Singular Integral Equations
5 A Priori Estimates of the Solution to the NSP
6 Uniqueness of the Solution to the NSP
7 The Paradox and Its Consequences
8 Logical Analysis of Our Proof
1 Theory of Distributions and Hyper-Singular Integrals
Gamma and Beta Functions
The Laplace Transform
Analysis of the Navier-Stokes Problem. Solution to the Millennium Problem Concerning the Navier-Stokes Equations
Introduction
Derivation of the Integral Inequality
Investigation of Integral Equations and Inequalities with Hyper-Singular Kernel
Uniqueness of the Solution to the NSP
Conclusions
Applications of Analytic Continuation to Tables of Integral Transforms and Some Integral Equations with Hyper-Singular Kernels
Introduction
More Examples
Some Applications
Conclusion
References
