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2D Vortex Motion of an Incompressible Ideal Fluid: The Koopman–von Neumann Approach

S. Albeverio

Institut für Angewandte Mathematik, Universität Bonn, Wegelerstr. 6, D-53115 Bonn SFB 611, Bonn, Germany

BiBoS, Bielefeld, CERFIM, Locarno and Acc. di Architettura, USI, Mendrisio, Switzerland

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and

B. Ferrario

Institut für Angewandte Mathematik, Universität Bonn, Wegelerstr. 6, D-53115 Bonn, Germany

On leave from Dipartimento di Matematica, Università di Pavia, via Ferrata 1, I-27100 Pavia, Italy.

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https://doi.org/10.1142/S0219025703001195Cited by:8 (Source: Crossref)

Abstract

An incompressible ideal fluid in the two-dimensional torus (i.e. the Euler equation in a rectangle with periodic boundary conditions) is considered. The flow for a vorticity field concentrated in any finite number of points is analyzed. A compound Poisson measure Π, invariant for this flow, is introduced. The Hilbert space ℒ²(Π) and the properties of the corresponding ℒ²-flow are investigated. In particular it is proven that the corresponding generator is Markov unique.

Keywords:

AMSC: 76B47, 76M23, 47D03, 60G60, 35Q05, 37A17, 47B25

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