Finite time singularities for the free boundary incompressible Euler equations

Pages 1061-1134 from Volume 178 (2013), Issue 3 by Angel Castro, Diego Córdoba, Charles Fefferman, Francisco Gancedo, Javier Gómez-Serrano

Abstract

In this paper, we prove the existence of smooth initial data for the 2D free boundary incompressible Euler equations (also known for some particular scenarios as the water wave problem) for which the smoothness of the interface breaks down in finite time into a splash singularity or a splat singularity.

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Keywords
, , , , ,
DOI
https://doi.org/10.4007/annals.2013.178.3.6
MR
3092476
zbMATH
06220729
Milestones
Received: 25 January 2012
Revised: 1 October 2012
Accepted: 16 November 2012
Published online: 1 November 2013

Authors

Angel Castro

École Normale Supérieure, Paris, France, Instituto de Ciencias Matemáticas, Madrid, Spain and Universidad Autónoma de Madrid, Madrid, Spain

Diego Córdoba

Consejo Superior de Investigaciones Científicas, Madrid, Spain

Charles Fefferman

Princeton University, Princeton, NJ

Francisco Gancedo

Universidad de Sevilla, Sevilla, Spain

Javier Gómez-Serrano

Consejo Superior de Investigaciones Científicas, Madrid, Spain and Princeton University, Princeton, NJ