Uniqueness of the 2D incompressible Euler equation on corner domains

We consider the 2D incompressible Euler equation on a corner domain with an angle between ¿/2 and ¿. In this setup, the uniqueness of solutions in the Yudovich class is not known in general due to the fact that the velocity is very far from being Lipschitz. In this work we prove that if the initial vorticity is non-negative and supported on one side of the angle bisector of the domain, then solutions in the Yudovich class are unique. This is the first result which proves uniqueness when the velocity is far from Lipschitz and the initial vorticity is nontrivial around the boundary. This is joint work with Andrea Nahmod.

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