  It has been known for some time that a 3D incompressible Euler flow that has
initially a barely smooth velocity field nonetheless has Lagrangian fluid
particle trajectories that are analytic in time for at least a finite time (Ph.
Serfati C.R. Acad. Sci. S\'erie I 320, 175-180 (1995); A. Shnirelman
arXiv:1205.5837 (2012)). Here an elementary derivation is given, based on
Cauchy's form of the Euler equations in Lagrangian coordinates. This form
implies simple recurrence relations among the time-Taylor coefficients of the
Lagrangian map, used here to derive bounds for the C^{1,\gamma} H\"older norms
of the coefficients and infer temporal analyticity of Lagrangian trajectories
when the initial velocity is C^{1,\gamma}.
