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arXiv · 1312.2917

On the absence of "splash" singularities in the case of two-fluid interfaces

Charles Fefferman·Alexandru D. Ionescu·Victor Lie
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Abstract

We show that "splash" singularities cannot develop in the case of locally smooth solutions of the two-fluid interface in two dimensions. More precisely, we show that the scenario of formation of singularities discovered by Castro-C\'{o}rdoba-Fefferman-Gancedo-G\'{o}mez-Serrano in the case of the water waves system, in which the interface remains locally smooth but self-intersects in finite time, is completely prevented in the case of two-fluid interfaces with positive densities.

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Charles Fefferman, Alexandru D. Ionescu, Victor Lie. 2013-12-10. On the absence of "splash" singularities in the case of two-fluid interfaces. https://doi.org/10.1215/00127094-3166629

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