{ "item_title" : "The Navier-Stokes Problem", "item_author" : [" Alexander G. Ramm "], "item_description" : "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.", "item_img_path" : "https://covers3.booksamillion.com/covers/bam/3/03/101/303/3031013034_b.jpg", "price_data" : { "retail_price" : "29.99", "online_price" : "29.99", "our_price" : "29.99", "club_price" : "29.99", "savings_pct" : "0", "savings_amt" : "0.00", "club_savings_pct" : "0", "club_savings_amt" : "0.00", "discount_pct" : "10", "store_price" : "" } }

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