Uniqueness of the 2D Euler equation on a corner domain with non-constant vorticity around the corner

We consider the 2D incompressible Euler equation on a corner domain ¿ with angle ¿¿ with $\frac{1}{2}< \nu < 1$. We prove that if the initial vorticity ¿0 ¿ L1(¿) ¿ L¿(¿) and if ¿0 is non-negative and supported on one side of the angle bisector of the domain, then the weak solutions are unique. This is the first result which proves uniqueness when the velocity is far from Lipschitz and the initial vorticity is non-constant around the boundary.A.N. is funded in part by NSF DMS-1800852 and the Simons Foundation Collaborations Grant on Wave Turbulence (Nahmod’s Award ID 651469