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 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 ,,,, ? 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, infinity). 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.