Annals of PDE

, 5:12 | Cite as

Splash Singularities for the Free Boundary Navier-Stokes Equations

  • Angel Castro
  • Diego Córdoba
  • Charles Fefferman
  • Francisco Gancedo
  • Javier Gómez-SerranoEmail author


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.


Singularities Splash Navier-Stokes Free boundary Incompressible 



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 Ramón 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 Ramón y Cajal program RyC-2010-07094, by the P12-FQM-2466 grant from Junta de Andalucía, 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.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Angel Castro
    • 1
    • 2
  • Diego Córdoba
    • 3
  • Charles Fefferman
    • 4
  • Francisco Gancedo
    • 5
  • Javier Gómez-Serrano
    • 6
    Email author
  1. 1.Departamento de Matemáticas, Facultad de CienciasUniversidad Autónoma de MadridMadridSpain
  2. 2.CSIC-UAM-UC3M-UCMInstituto de Ciencias MatemáticasMadridSpain
  3. 3.Consejo Superior de Investigaciones CientíficasInstituto de Ciencias MatemáticasMadridSpain
  4. 4.Department of MathematicsPrinceton UniversityPrincetonUSA
  5. 5.Departamento de Análisis Matemático and IMUSUniversidad de SevillaSevillaSpain
  6. 6.Department of MathematicsPrinceton UniversityPrincetonUSA

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