The Navier-Stokes Problem

By Alexander G. Ramm

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 ����(����, ����) 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 ���� ϵ ℝ+, 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(ℝ3) ? C(ℝ+) is proved, ����21(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.

• Format: Paperback
• Language: English
• ISBN: 3031013034
• ISBN13: 9783031013034
• Release Date: April 2021
• Publisher: Springer
• Length: 61 Pages
• Weight: 0.34 lbs.
• Dimensions: 0.2" x 7.5" x 9.3"