2D Vortex Motion of an Incompressible Ideal Fluid: The Koopman–von Neumann Approach-Reference-Cited by-同舟云学术

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

Published:2003-06 Issue:02 Volume:06 Page:155-165
ISSN:0219-0257
Container-title:Infinite Dimensional Analysis, Quantum Probability and Related Topics
language:en
Short-container-title:Infin. Dimens. Anal. Quantum. Probab. Relat. Top.

Author:

Albeverio S.¹²,Ferrario B.³

Affiliation:

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

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

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

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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Mathematical Physics,Statistics and Probability,Statistical and Nonlinear Physics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219025703001195

Reference17 articles.

1. Stationary measures for the periodic Euler flow in two dimensions

2. Uniqueness Results for the Generators of the Two-Dimensional Euler and Navier–Stokes Flows

3. Stochastic flows with stationary distribution for two-dimensional inviscid fluids

4. S. Albeverio, R. Høegh-Krohn and D. Merlini, Infinite-dimensional Analysis and Stochastic Processes, Euler flows, associated generalized random fields and Coulomb systems 124, ed. S. Albeverio (Pitman, 1985) pp. 216–244.

5. Dirichlet Operators via Stochastic Analysis

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