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We show that particle trajectories for positive vorticity solutions to the 2DEuler equations on fairly general bounded simply connected domains cannot reachthe boundary in finite time. This includes domains with possibly nowhere $C^1$boundaries and having corners with arbitrary angles, and can fail without thesign hypothesis when the domain has large angle corners. Hence positivevorticity solutions on such domains are Lagrangian, and we also obtain theiruniqueness if the vorticity is initially constant near the boundary.

Uniqueness of Positive Vorticity Solutions to the 2D Euler Equations on Singular Domains