Wellposedness and singularity formation beyond the Yudovich class

In this talk I will present recent results obtained in collaboration with Tarek M. Elgindi and Ryan M. Murray. We give a new supercritical class of data for the 2D Euler equation that allows for unbounded vorticities well beyond the Yudovich class. Within this class, we can demonstrate local existence and uniqueness of the solutions. Furthermore, we construct data for which a finite-time blow-up occurs. Leveraging the singularity formation we give an example of a finite time bifurcation for weak solutions of the 2d Euler equation in $L^p_{loc}(\mathbb{R}^2)$ for $p>1$.