U. Frisch, V. Zheligovsky
In 1994, Ph. Serfati showed 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. This result was recently revisited by A. Shnirelman. Here an elementary derivation is based on Cauchy's form of the Euler equations in Lagrangian coordinates. As shown by U. Frisch and T. Matsumoto, 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} Holder norms of the coefficients and infer temporal analyticity of Lagrangian trajectories when the initial velocity is C^{1,gamma}.
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http://arxiv.org/abs/1212.4333
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