The Navier–Stokes Problem
Seiten
2021
Morgan & Claypool Publishers (Verlag)
978-1-63639-122-9 (ISBN)
Morgan & Claypool Publishers (Verlag)
978-1-63639-122-9 (ISBN)
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The main result of this book is a proof of the contradictory nature of the NavierStokes problem (NSP). It is proved that the NSP is physically wrong, and the solution to the NSP does not exist on + (except for the case when the initial velocity and the exterior force are both equal to zero).
The main result of this book is a proof of the contradictory nature of the Navier—Stokes problem (NSP). It is proved that the NSP is physically wrong, and the solution to the NSP does not exist on ℝ+ (except for the case when the initial velocity and the exterior force are both equal to zero; in this case, the solution 𝑣(𝑥, 𝑡) to the NSP exists for all 𝑡 ≥ 0 and 𝑣(𝑥, 𝑡) = 0).It is shown that if the initial data 𝑣0(𝑥) ≢ 0, 𝑓(𝑥,𝑡) = 0 and the solution to the NSP exists for all 𝑡 ϵ ℝ+, then 𝑣0(𝑥) := 𝑣(𝑥, 0) = 0.
This Paradox proves that the NSP is physically incorrect and mathematically unsolvable, in general. Uniqueness of the solution to the NSP in the space 𝑊21(ℝ3) × C(ℝ+) is proved, 𝑊21(ℝ3) is the Sobolev space, ℝ+ = [0, ∞).
Theory of integral equations and inequalities with hyper-singular kernels is developed. The NSP is reduced to an integral inequality with a hyper-singular kernel.
The main result of this book is a proof of the contradictory nature of the Navier—Stokes problem (NSP). It is proved that the NSP is physically wrong, and the solution to the NSP does not exist on ℝ+ (except for the case when the initial velocity and the exterior force are both equal to zero; in this case, the solution 𝑣(𝑥, 𝑡) to the NSP exists for all 𝑡 ≥ 0 and 𝑣(𝑥, 𝑡) = 0).It is shown that if the initial data 𝑣0(𝑥) ≢ 0, 𝑓(𝑥,𝑡) = 0 and the solution to the NSP exists for all 𝑡 ϵ ℝ+, then 𝑣0(𝑥) := 𝑣(𝑥, 0) = 0.
This Paradox proves that the NSP is physically incorrect and mathematically unsolvable, in general. Uniqueness of the solution to the NSP in the space 𝑊21(ℝ3) × C(ℝ+) is proved, 𝑊21(ℝ3) is the Sobolev space, ℝ+ = [0, ∞).
Theory of integral equations and inequalities with hyper-singular kernels is developed. The NSP is reduced to an integral inequality with a hyper-singular kernel.
Preface
Introduction
Brief History of the Navier–Stokes Problem
Statement of the Navier–Stokes Problem
Theory of Some Hyper-Singular Integral Equations
A Priori Estimates of the Solution to the NSP
Uniqueness of the Solution to the NSP
The Paradox and its Consequences
Logical Analysis of Our Proof
Appendix 1 – Theory of Distributions and Hyper-Singular Integrals
Appendix 2 – Gamma and Beta Functions
Appendix 3 – The Laplace Transform
Bibliography
Author's Biography
| Erscheinungsdatum | 28.04.2021 |
|---|---|
| Reihe/Serie | Synthesis Lectures on Mathematics and Statistics |
| Verlagsort | San Rafael |
| Sprache | englisch |
| Maße | 191 x 235 mm |
| Gewicht | 333 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| Mathematik / Informatik ► Mathematik ► Analysis | |
| Mathematik / Informatik ► Mathematik ► Angewandte Mathematik | |
| ISBN-10 | 1-63639-122-2 / 1636391222 |
| ISBN-13 | 978-1-63639-122-9 / 9781636391229 |
| Zustand | Neuware |
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Buch | Softcover (2022)
Springer Spektrum (Verlag)
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