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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, Cordoba, Fefferman, Gancedo, and Gomez-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.|
|Electronic Publication Date:||5-Nov-2015|
|Citation:||Fefferman, Charles, Ionescu, Alexandru D, Lie, Victor. (2016). ON THE ABSENCE OF SPLASH SINGULARITIES IN THE CASE OF TWO-FLUID INTERFACES. DUKE MATHEMATICAL JOURNAL, 165 (417 - 462. doi:10.1215/00127094-3166629|
|Pages:||417 - 462|
|Type of Material:||Journal Article|
|Journal/Proceeding Title:||DUKE MATHEMATICAL JOURNAL|
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