The Navier-Stokes Problem (Heftet)

Serie: Synthesis Lectures on Mathematics and Statistics 


Innbinding: Heftet
Utgivelsesår: 2021
Antall sider: 77
Forlag: Morgan & Claypool Publishers
Språk: Engelsk
ISBN/EAN: 9781636391229
Kategori: Matematikk
Omtale The Navier-Stokes Problem
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 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 +, 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( 3) x C( +) is proved, 𝑊21( 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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