@article{ee42064d7b2d4d47b14fd2a606ee5378,
title = "Splash Singularities for the Free Boundary Navier-Stokes Equations",
abstract = "In this paper, we prove the existence of smooth initial data for the 2D free boundary incompressible Navier-Stokes equations, for which the smoothness of the interface breaks down in finite time into a splash singularity.",
keywords = "Free boundary, Incompressible, Navier-Stokes, Singularities, Splash",
author = "Angel Castro and Diego C{\'o}rdoba and Charles Fefferman and Francisco Gancedo and Javier G{\'o}mez-Serrano",
note = "Funding Information: AC, DC, CF, FG and JGS were partially supported by the grants MTM2011-26696, MTM2014-59488-P (Spain) and ICMAT Severo Ochoa projects SEV-2011-0087 and SEV-2015-0554. AC was partially supported by the Ram?n y Cajal program RyC-2013-14317 and ERC grant 307179-GFTIPFD. CF was partially supported by NSF grant DMS-1265524. FG was partially supported by the Ram?n y Cajal program RyC-2010-07094, by the P12-FQM-2466 grant from Junta de Andaluc?a, Spain and by the ERC Grant H2020-EU.1.1.-639227. JGS was partially supported by the Simons Collaboration Grant 524109 and by the NSF grant DMS-1763356. We thank the anonymous referee for his or her useful comments on previous versions of this manuscript. Funding Information: AC, DC, CF, FG and JGS were partially supported by the grants MTM2011-26696, MTM2014-59488-P (Spain) and ICMAT Severo Ochoa projects SEV-2011-0087 and SEV-2015-0554. AC was partially supported by the Ram{\'o}n y Cajal program RyC-2013-14317 and ERC grant 307179-GFTIPFD. CF was partially supported by NSF grant DMS-1265524. FG was partially supported by the Ram{\'o}n y Cajal program RyC-2010-07094, by the P12-FQM-2466 grant from Junta de Andaluc{\'i}a, Spain and by the ERC Grant H2020-EU.1.1.-639227. JGS was partially supported by the Simons Collaboration Grant 524109 and by the NSF grant DMS-1763356. We thank the anonymous referee for his or her useful comments on previous versions of this manuscript. Publisher Copyright: {\textcopyright} 2019, Springer Nature Switzerland AG.",
year = "2019",
month = jun,
day = "1",
doi = "10.1007/s40818-019-0068-1",
language = "English (US)",
volume = "5",
journal = "Annals of PDE",
issn = "2524-5317",
publisher = "Springer Science + Business Media",
number = "1",
}