Communications in Mathematical Physics

, Volume 129, Issue 3, pp 431–444 | Cite as

Global flows with invariant (Gibbs) measures for Euler and Navier-Stokes two dimensional fluids

  • Sergio Albeverio
  • Ana-Bela Cruzeiro


We construct a family of probability spacesΩℱ,Pγ), γ<0 associated with the Euler equation for a two dimensional inviscid incompressible fluid which carries a pointwise flow φt (time evolution) leavingPγ globally invariant. φt is obtained as the limit of Galerkin approximations associated with Euler equations.Pγ is also in invariant measure for a stochastic process associated with a Navier-Stokes equation with viscosity, γ, stochastically perturbed by a white noise force.


Viscosity Neural Network Statistical Physic Complex System Time Evolution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • Sergio Albeverio
    • 1
    • 2
  • Ana-Bela Cruzeiro
    • 3
  1. 1.Fakultät für MathematikRuhr-Universität-BochumBochumFederal Republic of Germany
  2. 2.BiBoS Research Centre and SFB 237Bochum-Essen-DüsseldorfFederal Republic of Germany
  3. 3.Centre de Matemática e Aplicações FundamentaisI.N.I.C.Lisboa CodexPortugal

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