Comment on On the flow map for 2D Euler equations with unbounded vorticity, Nonlinearity, 24(9), 2599-2637, 2011

As regards a comment in the middle of the proof of Theorem 3.1 (page 2607 in the published version), the time reversibility of the Euler equations is not the reason that the bound on the modulus of continuity of the reverse flow map is the same as that on the forward flow map. Rather, this is a more basic and universal property that holds whenever a velocity field has a bound on its modulus of continuity that is uniform over time. See, for instance, flow maps estimates for a non-autonomous vector field.