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The Navier-Stokes Problem - Alexander G. Ramm

The Navier-Stokes Problem

By: Alexander G. Ramm

eText | 1 June 2022

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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 ? (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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