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03291aam a2200433 i 4500 001 9CEAE3D2462211E9A3F20F6897128E48 003 SILO 005 20190314012734 008 181107t20182018riua b 000 0 eng 010 $a 2018053448 020 $a 1470431033 020 $a 9781470431037 035 $a (OCoLC)1048945902 040 $a DLC $b eng $e rda $c DLC $d OCLCO $d OCLCF $d YDX $d PAU $d STF $d MNU $d NUI $d SILO 042 $a pcc 100 1 $a Ionescu, Alexandru Dan, $d 1973- $e author. 245 10 $a Global regularity for 2D water waves with surface tension / $c Alexandru D. Ionescu, Fabio Pusateri. 264 1 $a Providence, RI : $b American Mathematical Society, $c [2018] 300 $a v, 123 pages ; $c 26 cm. 490 1 $a Memoirs of the American Mathematical Society, $x 0065-9266 ; $v number 1227 500 $a "November 2018, volume 256, number 1227 (third of 6 numbers)." 504 $a Includes bibliographical references (pages 121-123). 505 00 $t Elliptic bounds. $t Introduction -- $g Appendix C. $t Preliminaries -- $g Chapter 3. $t Derivation of the main scalar equation -- $g Chapter 4. $t Energy estimates I: high Sobolev estimates -- $g Chapter 5. $t Energy estimates II: low frequencies -- $g Chapter 6. $t Energy estimates III: Weighted estimates for high frequencies -- $g Chapter 7. $t Energy estimates IV: Weighted estimates for low frequencies -- $g Chapter 8. $t Decay estimates -- $g Chapter 9. $t Proof of Lemma 8.6 -- $g Chapter 10. $t Modified scattering -- $g Appendix A. $t Analysis of symbols -- $g Appendix B. $t The Dirichlet-Neumann operator -- $g Appendix C. $t Elliptic bounds. 520 $a "We consider the full irrotatioal water waves system with surface tension and no gravity in dimension two (the capillary waves system), and prove global regularity and modified scattering for suitably small and localized perturbations of a flat interface. An important point of our analysis is to develop a sufficiently robust method, based on energy estimates and dispersive analysis, which allows us to deal simultaneously with strong singularities arising from time resonances in the applications of the normal form method and with nonlinear scattering. As a result, we are able to consider a suitable class of perturbations with finite energy, but no other momentum conditions. Part of our analysis relies on a new treatment of the Dirichlet-Neumann operator in dimension two which is of independent interest. As a consequence, the results in this paper are self-contained."--Page v. 650 0 $a Waves $x Mathematical models. 650 0 $a Water waves $x Mathematical models. 650 0 $a Capillarity. 650 0 $a Surface tension. 650 7 $a Capillarity. $2 fast $0 (OCoLC)fst00846265 650 7 $a Surface tension. $2 fast $0 (OCoLC)fst01139242 650 7 $a Water waves $x Mathematical models. $2 fast $0 (OCoLC)fst01172256 650 7 $a Waves $x Mathematical models. $2 fast $0 (OCoLC)fst01172908 700 1 $a Pusateri, Fabio, $d 1983- $e author. 773 0 $t Memoirs of the American Mathematical Society $w 9954324590001701 $g no:1227 773 18 $w 990007620060202771 $g no:31858069689416 830 0 $a Memoirs of the American Mathematical Society ; $v no. 1227, $x 0065-9266 941 $a 1 952 $l OVUX522 $d 20191122013252.0 956 $a http://locator.silo.lib.ia.us/search.cgi?index_0=id&term_0=9CEAE3D2462211E9A3F20F6897128E48Initiate Another SILO Locator Search