1205.5837 (Alexander Shnirelman)

On the Analyticity of Particle Trajectories in the Ideal Incompressible
Fluid    [PDF]

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