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The NavierStokes Problem
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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.
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