Tuesday, May 29, 2012

1205.5837 (Alexander Shnirelman)

On the Analyticity of Particle Trajectories in the Ideal Incompressible

Alexander Shnirelman
A new proof is given of the fact that the particle trajectories of the ideal incompressible fluid are analytic curves, though the solutions of the Euler equations may have a finite regularity. This is a consequence of a general fact that the geodesic exponential map on the group of volume preserving diffeomorphisms belonging to the Sobolev space is real-analytic. The proof is based on the general properties of holomorphic maps in complex Banach spaces.
View original: http://arxiv.org/abs/1205.5837

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