English

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

Analysis of PDEs 2016-03-16 v2

Abstract

We show that "splash" singularities cannot develop in the case of locally smooth solutions of the two-fluid interface in two dimensions. More precisely, we show that the scenario of formation of singularities discovered by Castro-C\'{o}rdoba-Fefferman-Gancedo-G\'{o}mez-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.

Keywords

Cite

@article{arxiv.1312.2917,
  title  = {On the absence of "splash" singularities in the case of two-fluid interfaces},
  author = {Charles Fefferman and Alexandru D. Ionescu and Victor Lie},
  journal= {arXiv preprint arXiv:1312.2917},
  year   = {2016}
}

Comments

Replaced the file to correct misprints