Finite time singularities for the free boundary incompressible Euler equations

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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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