Duke Math. J. 165 (3), 417-462, (15 February 2016) DOI: 10.1215/00127094-3166629
Charles Fefferman, Alexandru D. Ionescu, Victor Lie
KEYWORDS: Euler equations, two-fluid interface, $2$-fluid interface, singularity formation, 35Q35, 76B15
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.