Abstract: In this talk, I will discuss 2D free boundary incompressible Euler equations with surface tension. We construct initial data with a flat free boundary and arbitrarily small velocity, such that the gradient of vorticity grows at least double-exponentially for all times during the lifespan of the corresponding solution. This work generalizes the celebrated result by Kiselev–Šverák to the free boundary setting. The free boundary introduces some major challenges in the proof due to the deformation of the fluid domain and the fact that the velocity field cannot be reconstructed from the vorticity using the Biot-Savart law. We overcome these issues by deriving uniform-in-time control on the free boundary and obtaining pointwise estimates on an approximate Biot-Savart law. This is joint work with Chenyun Luo and Yao Yao.