LEADER 03270nam 22004455a 450 001 9910151927803321 005 20120207234510.0 010 $a3-03719-606-8 024 70$a10.4171/106 035 $a(CKB)3710000000953880 035 $a(CH-001817-3)146-120207 035 $a(PPN)178156051 035 $a(EXLCZ)993710000000953880 100 $a20120207j20120209 fy 0 101 0 $aeng 135 $aurnn|mmmmamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aConcentration Compactness for Critical Wave Maps$b[electronic resource] /$fJoachim Krieger, Wilhelm Schlag 210 3 $aZuerich, Switzerland $cEuropean Mathematical Society Publishing House$d2012 215 $a1 online resource (490 pages) 225 0 $aEMS Monographs in Mathematics (EMM) ;$x2523-5192 330 $aWave maps are the simplest wave equations taking their values in a Riemannian manifold $(M,g)$. Their Lagrangian is the same as for the scalar equation, the only difference being that lengths are measured with respect to the metric $g$. By Noether's theorem, symmetries of the Lagrangian imply conservation laws for wave maps, such as conservation of energy. In coordinates, wave maps are given by a system of semilinear wave equations. Over the past 20 years important methods have emerged which address the problem of local and global wellposedness of this system. Due to weak dispersive effects, wave maps defined on Minkowski spaces of low dimensions, such as $\mathbb R^{2+1}_{t,x}$, present particular technical difficulties. This class of wave maps has the additional important feature of being energy critical, which refers to the fact that the energy scales exactly like the equation. Around 2000 Daniel Tataru and Terence Tao, building on earlier work of Klainerman-Machedon, proved that smooth data of small energy lead to global smooth solutions for wave maps from 2+1 dimensions into target manifolds satisfying some natural conditions. In contrast, for large data, singularities may occur in finite time for $M =\mathbb S^2$ as target. This monograph establishes that for $\mathbb H$ as target the wave map evolution of any smooth data exists globally as a smooth function. While we restrict ourselves to the hyperbolic plane as target the implementation of the concentration-compactness method, the most challenging piece of this exposition, yields more detailed information on the solution. This monograph will be of interest to experts in nonlinear dispersive equations, in particular to those working on geometric evolution equations. 606 $aDifferential equations$2bicssc 606 $aDifferential & Riemannian geometry$2bicssc 606 $aPartial differential equations$2msc 606 $aDifferential geometry$2msc 615 07$aDifferential equations 615 07$aDifferential & Riemannian geometry 615 07$aPartial differential equations 615 07$aDifferential geometry 686 $a35-xx$a53-xx$2msc 700 $aKrieger$b Joachim$01071019 702 $aSchlag$b Wilhelm 801 0$bch0018173 906 $aBOOK 912 $a9910151927803321 996 $aConcentration Compactness for Critical Wave Maps$92565659 997 $aUNINA LEADER 01170nam0-2200349---450 001 990005335270403321 005 20230217132129.0 035 $a000533527 100 $a19990604d1928----km-y0itay50------ba 101 0 $aeng 102 $aGB 105 $aabf-b---001-y 200 1 $a<>guide to the Departement of Greek and Roman antiquities in the British Museum$f[British Museum] 205 $a6th ed. 210 $aLondon$cOder of the Trustees$d1928 215 $aVII, 205 p.$c18 tav.$d22 cm 300 $aPrefazione di H. B. Walters 610 0 $aArte etrusca 610 0 $aVasi greci 610 0 $aAntichitą classiche 610 0 $aLondra$aBritish Museum$aCataloghi 610 0 $aSculture classiche$aCollezioni 676 $a708.212$v22$zita 702 1$aWalters,$bHenry Beauchamp$f<1867-1944> 710 02$aBritish Museum.$bDepartement of Greek and Roman antiquities$0294765 801 0$aIT$bUNINA$gREICAT$2UNIMARC 901 $aBK 912 $a990005335270403321 952 $a708.1 BRIM 03$bARCH. 13786$fFLFBC 959 $aFLFBC 996 $aGuide to the Departement of Greek and Roman antiquities in the British Museum$9599710 997 $aUNINA