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The Navier–Stokes Problem
About This Book
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 ?+ (except for the case when the initial velocity and the exterior force are both equal to zero; in this case, the solution (, ) to the NSP exists for all ? 0 and (, ) = 0). It is shown that if the initial data 0() ? 0, (, ) = 0 and the solution to the NSP exists for all ? ?+, then 0(): = (, 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 21(?3) × C(?+) is proved, 21(?3) is the Sobolev space, ?+ = [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.
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Table of contents
- Cover
- Copyright Page
- Title Page
- Dedication
- Contents
- Preface
- Introduction
- Brief History of the Navier–Stokes Problem
- Statement of the Navier–Stokes Problem
- A Priori Estimates of the Solution to the NSP
- 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
- Bibliography
- Author's Biography