LEADER 07109nam 22018135 450 001 9910163942603321 005 20230810001709.0 010 $a1-4008-8542-6 024 7 $a10.1515/9781400885428 035 $a(CKB)3710000001012298 035 $a(MiAaPQ)EBC4854432 035 $a(StDuBDS)EDZ0001756493 035 $a(DE-B1597)477784 035 $a(OCoLC)968415598 035 $a(OCoLC)979595921 035 $a(DE-B1597)9781400885428 035 $a(EXLCZ)993710000001012298 100 $a20190708d2017 fg 101 0 $aeng 135 $aurcnu|||||||| 181 $2rdacontent 182 $2rdamedia 183 $2rdacarrier 200 10$aHölder Continuous Euler Flows in Three Dimensions with Compact Support in Time /$fPhilip Isett 210 1$aPrinceton, NJ : $cPrinceton University Press, $d[2017] 210 4$d©2017 215 $a1 online resource (214 pages) 225 0 $aAnnals of Mathematics Studies ;$v357 300 $aPreviously issued in print: 2017. 311 $a0-691-17483-0 311 $a0-691-17482-2 320 $aIncludes bibliographical references and index. 327 $tFrontmatter -- $tContents -- $tPreface -- $tPart I. Introduction -- $tPart II. General Considerations of the Scheme -- $tPart III. Basic Construction of the Correction -- $tPart IV. Obtaining Solutions from the Construction -- $tPart V. Construction of Regular Weak Solutions: Preliminaries -- $tPart VI Construction of Regular Weak Solutions: Estimating the Correction -- $tPart VII. Construction of Regular Weak Solutions: Estimating the New Stress -- $tAcknowledgments -- $tAppendices -- $tReferences -- $tIndex 330 $aMotivated by the theory of turbulence in fluids, the physicist and chemist Lars Onsager conjectured in 1949 that weak solutions to the incompressible Euler equations might fail to conserve energy if their spatial regularity was below 1/3-Hölder. In this book, Philip Isett uses the method of convex integration to achieve the best-known results regarding nonuniqueness of solutions and Onsager's conjecture. Focusing on the intuition behind the method, the ideas introduced now play a pivotal role in the ongoing study of weak solutions to fluid dynamics equations.The construction itself-an intricate algorithm with hidden symmetries-mixes together transport equations, algebra, the method of nonstationary phase, underdetermined partial differential equations (PDEs), and specially designed high-frequency waves built using nonlinear phase functions. The powerful "Main Lemma"-used here to construct nonzero solutions with compact support in time and to prove nonuniqueness of solutions to the initial value problem-has been extended to a broad range of applications that are surveyed in the appendix. Appropriate for students and researchers studying nonlinear PDEs, this book aims to be as robust as possible and pinpoints the main difficulties that presently stand in the way of a full solution to Onsager's conjecture. 410 0$aAnnals of mathematics studies ;$vNumber 196. 606 $aFluid dynamics$xMathematics 610 $aBeltrami flows. 610 $aEinstein summation convention. 610 $aEuler equations. 610 $aEuler flow. 610 $aEuler-Reynolds equations. 610 $aEuler-Reynolds system. 610 $aGalilean invariance. 610 $aGalilean transformation. 610 $aHigh?igh Interference term. 610 $aHigh?igh term. 610 $aHigh?ow Interaction term. 610 $aHlder norm. 610 $aHlder regularity. 610 $aLars Onsager. 610 $aMain Lemma. 610 $aMain Theorem. 610 $aMollification term. 610 $aNewton's law. 610 $aNoether's theorem. 610 $aOnsager's conjecture. 610 $aReynolds stres. 610 $aReynolds stress. 610 $aStress equation. 610 $aStress term. 610 $aTransport equation. 610 $aTransport term. 610 $aTransport-Elliptic equation. 610 $aabstract index notation. 610 $aalgebra. 610 $aamplitude. 610 $acoarse scale flow. 610 $acoarse scale velocity. 610 $acoefficient. 610 $acommutator estimate. 610 $acommutator term. 610 $acommutator. 610 $aconservation of momentum. 610 $acontinuous solution. 610 $acontravariant tensor. 610 $aconvergence. 610 $aconvex integration. 610 $acorrection term. 610 $acorrection. 610 $acovariant tensor. 610 $adimensional analysis. 610 $adivergence equation. 610 $adivergence free vector field. 610 $adivergence operator. 610 $aenergy approximation. 610 $aenergy function. 610 $aenergy increment. 610 $aenergy regularity. 610 $aenergy variation. 610 $aenergy. 610 $aerror term. 610 $aerror. 610 $afinite time interval. 610 $afirst material derivative. 610 $afluid dynamics. 610 $afrequencies. 610 $afrequency energy levels. 610 $ah-principle. 610 $aintegral. 610 $alifespan parameter. 610 $alower indices. 610 $amaterial derivative. 610 $amollification. 610 $amollifier. 610 $amoment vanishing condition. 610 $amomentum. 610 $amulti-index. 610 $anon-negative function. 610 $anonzero solution. 610 $aoptimal regularity. 610 $aoscillatory factor. 610 $aoscillatory term. 610 $aparameters. 610 $aparametrix expansion. 610 $aparametrix. 610 $aphase direction. 610 $aphase function. 610 $aphase gradient. 610 $apressure correction. 610 $apressure. 610 $aregularity. 610 $arelative acceleration. 610 $arelative velocity. 610 $ascaling symmetry. 610 $asecond material derivative. 610 $asmooth function. 610 $asmooth stress tensor. 610 $asmooth vector field. 610 $aspatial derivative. 610 $astress. 610 $atensor. 610 $atheorem. 610 $atime cutoff function. 610 $atime derivative. 610 $atransport derivative. 610 $atransport equations. 610 $atransport estimate. 610 $atransport. 610 $aupper indices. 610 $avector amplitude. 610 $avelocity correction. 610 $avelocity field. 610 $avelocity. 610 $aweak limit. 610 $aweak solution. 615 0$aFluid dynamics$xMathematics. 676 $a532/.05 700 $aIsett$b Philip, $01223707 801 0$bDE-B1597 801 1$bDE-B1597 906 $aBOOK 912 $a9910163942603321 996 $aHölder Continuous Euler Flows in Three Dimensions with Compact Support in Time$92839606 997 $aUNINA