Cohen–Danchin logarithmic-sharpness conjecture for acute-corner cusps

Consider a vortex patch whose boundary has a single corner of acute angle, and define the order of a cusp at $x=x_0$ by

$$\sup\left\{\beta>0:\limsup_{x\to x_0}\frac{|(f_1-f_2)(x)|}{|x-x_0|^{\beta}}<\infty\right\},$$

where $f_1$ and $f_2$ represent the graphs of the two sides of the cusping boundary near $x=x_0$. Cohen–Danchin's conjecture. Any acute single corner would immediately evolve into a cusp of order $1$ with logarithmic sharpness. The conjecture refines the prediction that an acute corner immediately forms a cusp, using the fact stated in the source that cusps of order one are preserved in time.