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The Navier–Stokes Problem
Alexander G. Ramm
出版Springer Nature, 2022-06-01
主題Mathematics / GeneralMathematics / Probability & Statistics / GeneralTechnology & Engineering / Engineering (General)Mathematics / Applied
ISBN30310243119783031024313
URLhttp://books.google.com.hk/books?id=IYByEAAAQBAJ&hl=&source=gbs_api
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註釋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.