Finite time singularities for the free boundary incompressible Euler equations

By A. Castro, D. C'ordoba, Charles Fefferman, Francisco Gancedo, Javier G'omez-Serrano. 2011

139 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Earth-Surface Processes, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/6b36e74ad6f5b4c21bdf68df76b19b3f260b9498

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In Applied Mathematics

In Earth-Surface Processes

In Mathematical Physics

Citations in the corpus

Global solutions and asymptotic behavior for two dimensional gravity water waves (2013, result): “self-intersects. Notice that, according to this conjecture, one does not expect global well-posedness for arbitrarily large initial data. One can quote several results supporting this conjecture (see [14, 16, 21]). In [14] (see also [21]), the authors prove the following result: there exists an init”
Finite time singularity for the modified SQG patch equation (2016, result): “We refer to [5], [4], [54], [55] for other recent advances in some of the interface problems of fluid dynamics.”
On the Cauchy problem for gravity water waves (2012, background): “work in the study of the Cauchy problem for the water waves system in arbitrary dimension, without surface tension. An important question in the theory is the possible emergence of singularities (see [16, 17, 20, 25, 58]) and as emphasized by Craig and Wayne [30], it is important to decide whether s”