A Very Smooth Ride in a Rough Sea View Full Text


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Article Info

DATE

2014-03

AUTHORS

Uriel Frisch, Vladislav Zheligovsky

ABSTRACT

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 Série 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 C1,γ Hölder norms of the coefficients and infer temporal analyticity of Lagrangian trajectories when the initial velocity is C1,γ. More... »

PAGES

499-505

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00220-013-1848-1

DOI

http://dx.doi.org/10.1007/s00220-013-1848-1

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1052252255


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