TY - JOUR
T1 - On the absence of splash singularities in the case of two-fluid interfaces
AU - Fefferman, Charles
AU - Ionescu, Alexandru D.
AU - Lie, Victor
N1 - Funding Information: Ionescu would like to thank Fabio Pusateri for several useful discussions on the topic. Fefferman''s work was partially supported by National Science Foundation grant DMS-0901040. Ionescu''s work was partially supported by a Packard Fellowship and by National Science Foundation grant DMS-1265818. Lie''s work was partially supported by National Science Foundation grant DMS-0100932. Publisher Copyright: © 2016.
PY - 2016
Y1 - 2016
N2 - 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.
AB - 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.
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U2 - 10.1215/00127094-3166629
DO - 10.1215/00127094-3166629
M3 - Article
SN - 0012-7094
VL - 165
SP - 417
EP - 462
JO - Duke Mathematical Journal
JF - Duke Mathematical Journal
IS - 3
ER -