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}
}
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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