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Equilibrium states for a plane incompressible perfect fluid

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Abstract

We associate to the plane incompressible Euler equation with periodic conditions the corresponding Hopf equation, as an equation for measures on the space of solenoidal distributions. We define equilibrium states as the solutions of the stationary Hopf equation. We find a class of equilibrium states which corresponds to a class of infinitely divisible distributions, and investigate the properties of gaussian and poissonian states. Equilibrium dynamics for a class of poissonian states is constructed by means of the Onsager vortex equations.

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Authors and Affiliations

  1. Istituto Matematico, Università di Camerino, Camerino, Italy

    Carlo Boldrighini & Sandro Frigio

  2. C.N.R. fellowship, G.N.F.M., Italy

    Sandro Frigio

Authors
  1. Carlo Boldrighini
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  2. Sandro Frigio
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Communicated by J. L. Lebowitz

Research partially supported by C.N.R., G.N.F.M.

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Boldrighini, C., Frigio, S. Equilibrium states for a plane incompressible perfect fluid. Commun.Math. Phys. 72, 55–76 (1980). https://doi.org/10.1007/BF01200111

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  • DOI: https://doi.org/10.1007/BF01200111

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