| Abstract: |
| The Sadovskii vortex patch--a steady contiguous anti-symmetric vortex-patch dipole solution of the 2D incompressible Euler qquation--was numerically discovered over 50 years ago, whose was also observed as an accurate approximation of the large-time asymptotic profile in the head-on collision of two anti-symmetric vortex rings. In this talk, we present the first proof of existence of the Sadovskii vortex patch with 90-degree touching angles via a fixed-point approach. In particular, we show that the upper boundary of the Sadovskii vortex patch is given by a smooth even function that is monotonic on one side. |
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