000			09048nam a2200649Ii 4500
001			9781315373393
003			FlBoTFG
005			20220711212220.0
006			m o d
007			cr
008			181112t20182016flu b ob 001 0 eng d
020			_a9781315373393 _q(e-book : PDF)
035			_a(OCoLC)945678771
040			_aFlBoTFG _cFlBoTFG _erda
041	1		_aeng
050		4	_a QA901
052			_a518.64
072		7	_aMAT _x007000 _2bisacsh
072		7	_aSCI _x055000 _2bisacsh
072		7	_aTEC _x009070 _2bisacsh
072		7	_aPBKJ _2bicscc
082	0	4	_a 518/.64
100	1		_aLemarie-Rieusset, Pierre Gilles, _eauthor. _914376
245	1	4	_aThe Navier-Stokes Problem in the 21st Century / _cby Pierre Gilles Lemarie-Rieusset.
250			_aFirst edition.
264		1	_aBoca Raton, FL : _bChapman and Hall/CRC, _c[2018].
264		4	_c©2016.
300			_a1 online resource (740 pages)
336			_atext _2rdacontent
337			_acomputer _2rdamedia
338			_aonline resource _2rdacarrier
504			_aIncludes bibliographical references and index.
505	0	0	_tPresentation of the Clay Millennium Prizes--Regularity of the three-dimensional fluid flows: a mathematical challenge for the 21st century--The Clay Millennium Prizes--The Clay Millennium Prize for the NavierStokes equations--Boundaries and the NavierStokes Clay Millennium Problem -- _tThe physical meaning of the NavierStokes equations--Frames of references --The convection theorem--Conservation of mass --Newton's second law --Pressure--Strain--Stress--The equations of hydrodynamics --The NavierStokes equations --Vorticity--Boundary terms --Blow up --Turbulence -- _tHistory of the equation--Mechanics in the Scientific Revolution era --Bernoulli's Hydrodymica--D'Alembert--Euler--Laplacian physics--Navier, Cauchy, Poisson, Saint-Venant, and Stokes --Reynolds --Oseen, Leray, Hopf, and Ladyzhenskaya--Turbulence models -- _tClassical solutions--The heat kernel --The Poisson equation --The Helmholtz decomposition --The Stokes equation --The Oseen tensor --Classical solutions for the NavierStokes problem--Small data and global solutions--Time asymptotics for global solutions--Steady solutions--Spatial asymptotics--Spatial asymptotics for the vorticity--Intermediate conclusion -- _tA capacitary approach of the NavierStokes integral equations--The integral NavierStokes problem--Quadratic equations in Banach spaces--A capacitary approach of quadratic integral equations --Generalized Riesz potentials on spaces of homogeneous type--Dominating functions for the NavierStokes integral equations--A proof of Oseen's theorem through dominating functions--Functional spaces and multipliers -- _tThe differential and the integral NavierStokes equations -- _tUniform local estimates --Heat equation --Stokes equations --Oseen equations --Very weak solutions for the NavierStokes equations --Mild solutions for the NavierStokes equations --Suitable solutions for the NavierStokes equations -- _tMild solutions in Lebesgue or Sobolev spaces -- _tKato's mild solutions--Local solutions in the Hilbertian setting --Global solutions in the Hilbertian setting --Sobolev spaces --A commutator estimate --Lebesgue spaces --Maximal functions--Basic lemmas on real interpolation spaces --Uniqueness of L3 solutions -- _tMild solutions in Besov or Morrey spaces -- _tMorrey spaces --Morrey spaces and maximal functions--Uniqueness of Morrey solutions--Besov spaces --Regular Besov spaces --TriebelLizorkin spaces --Fourier transform and NavierStokes equations -- _tThe space BMO-1 and the Koch and Tataru theorem -- _tKoch and Tataru's theorem--Q-spaces --A special subclass of BMO-1--Ill-posedness--Further results on ill-posedness --Large data for mild solutions --Stability of global solutions--Analyticity --Small data -- _tSpecial examples of solutions -- _tSymmetries for the NavierStokes equations--Two-and-a-half dimensional flows --Axisymmetrical solutions --Helical solutions --Brandolese's symmetrical solutions --Self-similar solutions--Stationary solutions --Landau's solutions of the NavierStokes equations--Time-periodic solutions --Beltrami flows -- _tBlow up? --First criteria--Blow up for the cheap NavierStokes equation --Serrin's criterion--Some further generalizations of Serrin's criterion--Vorticity --Squirts -- _tLeray's weak solutions--The Rellich lemma --Leray's weak solutions--Weak-strong uniqueness: the ProdiSerrin criterion--Weak-strong uniqueness and Morrey spaces on the product space R R3--Almost strong solutions --Weak perturbations of mild solutions -- _tPartial regularity results for weak solutions--Interior regularity --Serrin's theorem on interior regularity--O'Leary's theorem on interior regularity--Further results on parabolic Morrey spaces--Hausdorff measures --Singular times --The local energy inequality--The CaffarelliKohnNirenberg theorem on partial regularity--Proof of the CaffarelliKohnNirenberg criterion--Parabolic Hausdorff dimension of the set of singular points--On the role of the pressure in the Caffarelli, Kohn, and Nirenberg regularity theorem -- _tA theory of uniformly locally L2 solutions--Uniformly locally square integrable solutions--Local inequalities for local Leray solutions--The Caffarelli, Kohn, and Nirenberg -regularity criterion--A weak-strong uniqueness result -- _tThe L3 theory of suitable solutions--Local Leray solutions with an initial value in L3--Critical elements for the blow up of the Cauchy problem in L3--Backward uniqueness for local Leray solutions--Seregin's theorem--Known results on the Cauchy problem for the NavierStokes equations in presence of a force--Local estimates for suitable solutions--Uniqueness for suitable solutions--A quantitative one-scale estimate for the CaffarelliKohnNirenberg regularity criterion--The topological structure of the set of suitable solutions--Escauriaza, Seregin, and verk's theorem -- _tSelf-similarity and the LeraySchauder principle--The LeraySchauder principle--Steady-state solutions--Self-similarity--Statement of Jia and verk's theorem--The case of locally bounded initial data--The case of rough data--Non-existence of backward self-similar solutions -- _t---models--Global existence, uniqueness and convergence issues for approximated equations --Leray's mollification and the Leray- model--The NavierStokes -model--The Clark- model--The simplified Bardina model--Reynolds tensor -- _tOther approximations of the NavierStokes equations--FaedoGalerkin approximations --Frequency cut-off --Hyperviscosity --Ladyzhenskaya's model--Damped NavierStokes equations -- _tArtificial compressibility--Temam's model--Vishik and Fursikov's model --Hyperbolic approximation -- _tConclusion --Energy inequalities--Critical spaces for mild solutions--Models for the (potential) blow up--The method of critical elements -- _tNotations and glossary -- _tBibliography -- _tIndex.
520	3		_aUp-to-Date Coverage of the Navier-Stokes Equation from an Expert in Harmonic Analysis The complete resolution of the Navier-Stokes equation-one of the Clay Millennium Prize Problems-remains an important open challenge in partial differential equations (PDEs) research despite substantial studies on turbulence and three-dimensional fluids. The Navier-Stokes Problem in the 21st Century provides a self-contained guide to the role of harmonic analysis in the PDEs of fluid mechanics. The book focuses on incompressible deterministic Navier-Stokes equations in the case of a fluid filling the whole space. It explores the meaning of the equations, open problems, and recent progress. It includes classical results on local existence and studies criterion for regularity or uniqueness of solutions. The book also incorporates historical references to the (pre)history of the equations as well as recent references that highlight active mathematical research in the field.
530			_aAlso available in print format.
650		7	_aSCIENCE / Physics. _2bisacsh _910678
650		7	_aTECHNOLOGY & ENGINEERING / Mechanical. _2bisacsh _914377
650		7	_aCaffarelli, Kohn, and Nirenberg. _2bisacsh _914378
650		7	_aClay Millennium Prize Problems. _2bisacsh _914379
650		7	_acapacitary theory. _2bisacsh _914380
650		7	_afluid mechanics. _2bisacsh _92810
650		7	_aHarmonic Analysis. _2bisacsh _914381
650		7	_aLeray's weak solutions. _2bisacsh _914382
650		7	_aMorrey spaces. _2bisacsh _914383
650		7	_aNavier-Stokes equations. _2bisacsh _914384
650		7	_apartial differential equations. _2bisacsh _914385
650		0	_aFluid mechanics. _92810
650		0	_aNavier-Stokes equations. _914384
650		0	_aFluid dynamics. _94077
650		0	_aFluid dynamics _xMathematics. _914386
650		0	_aMATHEMATICS _xNumerical Analysis. _98877
655		0	_aElectronic books. _93294
710	2		_aTaylor and Francis. _910719
776	0	8	_iPrint version: _z9781466566217
856	4	0	_uhttps://www.taylorfrancis.com/books/9781315373393 _zClick here to view.
942			_cEBK
999			_c70691 _d70691