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

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Abstract

We show that so-called splash singularities cannot develop in the case of locally smooth solutions of the two-fluid interfaces in two dimensions. More precisely, we show that the scenario of formation of singularities discovered by Castro, Córdoba, Fefferman, Gancedo, and Gómez-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.

Original languageEnglish (US)
Pages (from-to)417-462
Number of pages46
JournalDuke Mathematical Journal
Volume165
Issue number3
DOIs
StatePublished - Jan 1 2016

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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