The Poincare Recurrence Problem of Inviscid Incompressible Fluids

Nadirashvili presented a beautiful example showing that the Poincaré recurrence does not occur near a particular solution to the 2D Euler equation of inviscid incompressible fluids. Unfortunately, Nadirashvili's setup of the phase space is not appropriate, and details of the proof are missing. This note fixes that.

Keywords

Poincaré recurrence, Euler equation of fluids, vorticity, Biot-Savart law, single layer potential

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Published 1 January 2009