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001			978-3-031-02431-3
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020			_a9783031024313 _9978-3-031-02431-3
024	7		_a10.1007/978-3-031-02431-3 _2doi
050		4	_aQA1-939
072		7	_aPB _2bicssc
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082	0	4	_a510 _223
100	1		_aRamm, Alexander G. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut _979036
245	1	4	_aThe Navier-Stokes Problem _h[electronic resource] / _cby Alexander G. Ramm.
250			_a1st ed. 2021.
264		1	_aCham : _bSpringer International Publishing : _bImprint: Springer, _c2021.
300			_aXV, 61 p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aSynthesis Lectures on Mathematics & Statistics, _x1938-1751
505	0		_aPreface -- Introduction -- Brief History of the Navier-Stokes Problem -- Statement of the Navier-Stokes Problem -- Theory of Some Hyper-Singular Integral Equations -- A Priori Estimates of the Solution to the NSP -- Uniqueness of the Solution to the NSP -- The Paradox and its Consequences -- Logical Analysis of Our Proof -- Appendix 1 - Theory of Distributions and Hyper-Singular Integrals -- Appendix 2 - Gamma and Beta Functions -- Appendix 3 - The Laplace Transform -- Bibliography -- Author's Biography.
520			_aThe 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.
650		0	_aMathematics. _911584
650		0	_aStatistics . _931616
650		0	_aEngineering mathematics. _93254
650	1	4	_aMathematics. _911584
650	2	4	_aStatistics. _914134
650	2	4	_aEngineering Mathematics. _93254
710	2		_aSpringerLink (Online service) _979037
773	0		_tSpringer Nature eBook
776	0	8	_iPrinted edition: _z9783031002779
776	0	8	_iPrinted edition: _z9783031013034
776	0	8	_iPrinted edition: _z9783031035593
830		0	_aSynthesis Lectures on Mathematics & Statistics, _x1938-1751 _979038
856	4	0	_uhttps://doi.org/10.1007/978-3-031-02431-3
912			_aZDB-2-SXSC
942			_cEBK
999			_c84703 _d84703