Euler Equations on General Planar Domains

We obtain a general sufficient condition on the geometry of possibly singular planar domains that guarantees global uniqueness for any weak solution to Euler equations them whose vorticity is bounded and initially constant near boundary. While similar existing results require are $$C^{1,1}$$ except at finitely many convex corners, our involves much less domain smoothness, being only slightly more restrictive than exclusion corners with angles greater $$\pi $$ . In particular, it satisfied by all domains. The main ingredient in approach showing constancy boundary preserved time because particle trajectories these domains, even solutions, cannot reach finite time. then use this show no can be created such solutions. also essentially sharp sense constructing come arbitrarily close satisfying it, which addition, when satisfied, we find bounds asymptotic rate fastest possible