期刊
COMMUNICATIONS IN MATHEMATICAL PHYSICS
卷 326, 期 2, 页码 499-505出版社
SPRINGER
DOI: 10.1007/s00220-013-1848-1
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资金
- Russian foundation for basic research [11-05-00167-a]
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 Serfati (C. R. Acad. Sci. Paris S,rie I 320:175-180, 1995), Shnirelman (Glob. Stoch. Anal., http://arxiv.org/abs/1205.5837v1, 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) Holder norms of the coefficients and infer temporal analyticity of Lagrangian trajectories when the initial velocity is C (1,gamma).
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