# Self-intersecting Interfaces for Stationary Solutions of the Two-Fluid Euler Equations

@article{Crdoba2019SelfintersectingIF,
title={Self-intersecting Interfaces for Stationary Solutions of the Two-Fluid Euler Equations},
author={D. C{\'o}rdoba and A. Enciso and Nastasia Grubic},
journal={Annals of PDE},
year={2019},
volume={7},
pages={1-40}
}
• Published 2019
• Mathematics, Physics
• Annals of PDE
We prove that there are stationary solutions to the 2D incompressible free boundary Euler equations with two fluids, possibly with a small gravity constant, that feature a splash singularity. More precisely, in the solutions we construct the interface is a $$\mathcal {C}^{2,\alpha }$$ C 2 , α  smooth curve that intersects itself at one point, and the vorticity density on the interface is of class  $$\mathcal {C}^\alpha$$ C α . The proof consists in perturbing Crapper’s family of formal… Expand
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