Navier-Stokes Problem

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; 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.