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15 February 2016 On the absence of splash singularities in the case of two-fluid interfaces
Charles Fefferman, Alexandru D. Ionescu, Victor Lie
Duke Math. J. 165(3): 417-462 (15 February 2016). DOI: 10.1215/00127094-3166629

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.

Citation

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Charles Fefferman. Alexandru D. Ionescu. Victor Lie. "On the absence of splash singularities in the case of two-fluid interfaces." Duke Math. J. 165 (3) 417 - 462, 15 February 2016. https://doi.org/10.1215/00127094-3166629

Information

Received: 23 December 2013; Revised: 24 March 2015; Published: 15 February 2016
First available in Project Euclid: 5 November 2015

zbMATH: 1346.35152
MathSciNet: MR3466160
Digital Object Identifier: 10.1215/00127094-3166629

Subjects:
Primary: 35Q35
Secondary: 76B15

Rights: Copyright © 2016 Duke University Press

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Vol.165 • No. 3 • 15 February 2016
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