Time-analyticity of Lagrangian particle trajectories in ideal fluid flow
  It is known that the Eulerian and Lagrangian structures of fluid flow can be
drastically different; for example, ideal fluid flow can have a trivial
(static) Eulerian structure, while displaying chaotic streamlines. Here we show
that ideal flow with limited spatial smoothness (an initial vorticity that is
just a little better than continuous), nevertheless has time-analytic
Lagrangian trajectories before the initial limited smoothness is lost. For
proving such results we use a little-known Lagrangian formulation of ideal
fluid flow derived by Cauchy in 1815 in a manuscript submitted for a prize of
the French Academy. This formulation leads to simple recurrence relations among
the time-Taylor coefficients of the Lagrangian map from initial to current
fluid particle positions; the coefficients can then be bounded using elementary
methods. We first consider various classes of incompressible fluid flow,
governed by the Euler equations, and then turn to a case of compressible flow
of cosmological relevance, governed by the Euler-Poisson equations.
