IUMJ

Title: Uniqueness for the 2-D Euler equations on domains with corners

Authors: Christophe Lacave, Evelyne Miot and Chao Wang

Issue: Volume 63 (2014), Issue 6, 1725-1756

Abstract:

We prove uniqueness of the solution of the Euler equations with bounded vorticity for bounded simply connected planar domains with corners forming acute angles. Our strategy consists in mapping such domains on the unit disk via a biholomorphism. We then establish $\log$-Lipschitz regularity for the resulting push-forward of the velocity field, which leads to uniqueness thanks to a Gronwall estimate involving the Lagrangian trajectories on the unit disk.