LEADER 04462nam 22006375 450 001 9910484145003321 005 20200705031628.0 010 $a3-030-36226-4 024 7 $a10.1007/978-3-030-36226-3 035 $a(CKB)4920000000496066 035 $a(DE-He213)978-3-030-36226-3 035 $a(MiAaPQ)EBC6284169 035 $a(PPN)243760809 035 $a(EXLCZ)994920000000496066 100 $a20200428d2020 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aMathematical Analysis of the Navier-Stokes Equations $eCetraro, Italy 2017 /$fby Matthias Hieber, James C. Robinson, Yoshihiro Shibata ; edited by Giovanni P. Galdi, Yoshihiro Shibata 205 $a1st ed. 2020. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2020. 215 $a1 online resource (VII, 464 p. 3 illus.) 225 1 $aC.I.M.E. Foundation Subseries ;$v2254 311 $a3-030-36225-6 327 $aGiovanni P. Galdi, Yoshihiro Shibata: Preface -- Matthias Hieber: Analysis of Viscous Fluid Flows: An Approach by Evolution Equations -- James C. Robinson: Partial regularity for the 3D Navier-Stokes equations -- Yoshihiro Shibata: R Boundedness, Maximal Regularity and Free Boundary Problems for the Navier Stokes Equations. 330 $aThis book collects together a unique set of articles dedicated to several fundamental aspects of the Navier?Stokes equations. As is well known, understanding the mathematical properties of these equations, along with their physical interpretation, constitutes one of the most challenging questions of applied mathematics. Indeed, the Navier?Stokes equations feature among the Clay Mathematics Institute's seven Millennium Prize Problems (existence of global in time, regular solutions corresponding to initial data of unrestricted magnitude). The text comprises three extensive contributions covering the following topics: (1) Operator-Valued H?-calculus, R-boundedness, Fourier multipliers and maximal Lp-regularity theory for a large, abstract class of quasi-linear evolution problems with applications to Navier?Stokes equations and other fluid model equations; (2) Classical existence, uniqueness and regularity theorems of solutions to the Navier?Stokes initial-value problem, along with space-time partial regularity and investigation of the smoothness of the Lagrangean flow map; and (3) A complete mathematical theory of R-boundedness and maximal regularity with applications to free boundary problems for the Navier?Stokes equations with and without surface tension. Offering a general mathematical framework that could be used to study fluid problems and, more generally, a wide class of abstract evolution equations, this volume is aimed at graduate students and researchers who want to become acquainted with fundamental problems related to the Navier?Stokes equations. 410 0$aC.I.M.E. Foundation Subseries ;$v2254 606 $aPartial differential equations 606 $aFluids 606 $aApplied mathematics 606 $aEngineering mathematics 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 606 $aFluid- and Aerodynamics$3https://scigraph.springernature.com/ontologies/product-market-codes/P21026 606 $aApplications of Mathematics$3https://scigraph.springernature.com/ontologies/product-market-codes/M13003 615 0$aPartial differential equations. 615 0$aFluids. 615 0$aApplied mathematics. 615 0$aEngineering mathematics. 615 14$aPartial Differential Equations. 615 24$aFluid- and Aerodynamics. 615 24$aApplications of Mathematics. 676 $a515.353 700 $aHieber$b Matthias$4aut$4http://id.loc.gov/vocabulary/relators/aut$065841 702 $aRobinson$b James C$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aShibata$b Yoshihiro$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aGaldi$b Giovanni P$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aShibata$b Yoshihiro$4edt$4http://id.loc.gov/vocabulary/relators/edt 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910484145003321 996 $aMathematical Analysis of the Navier-Stokes Equations$92212375 997 $aUNINA