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Abstract
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For a large class of non smooth bounded domains, existence of a global weak solution of the 2D
Euler equations, with bounded vorticity, was established by D. Gerard-Varet and C. Lacave. In the case of sharp domains, the question of uniqueness for such weak solutions is more involved due to the bad behavior close to the boundary. In the present work, we show uniqueness for any bounded and simply connected domain with a finite number of corners of angles smaller than /2. Our strategy relies on a Log-Lipschitz type regularity for the velocity field.
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