The Navier-Stokes Problem Hardback
by Alexander G. Ramm
Part of the Synthesis Lectures on Mathematics and Statistics series
Hardback
Description
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 â„+ (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 â„+, 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(â„3) × C(â„+) is proved, 𝑊21(â„3) is the Sobolev space, â„+ = [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.
Information
-
Item not Available
- Format:Hardback
- Pages:77 pages
- Publisher:Morgan & Claypool Publishers
- Publication Date:06/04/2021
- Category:
- ISBN:9781636391243
Other Formats
- Paperback / softback from £21.05
- PDF from £21.24
Information
-
Item not Available
- Format:Hardback
- Pages:77 pages
- Publisher:Morgan & Claypool Publishers
- Publication Date:06/04/2021
- Category:
- ISBN:9781636391243