On the Analyticity of Particle Trajectories in the Ideal Incompressible Fluid

Alexander Shnirelman

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arXiv · 1205.5837

On the Analyticity of Particle Trajectories in the Ideal Incompressible Fluid

Alexander Shnirelman

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Abstract

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.

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Alexander Shnirelman. 2012-05-25. On the Analyticity of Particle Trajectories in the Ideal Incompressible Fluid. https://arxiv.org/abs/1205.5837

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