Abstract
We construct a family of probability spacesΩℱ,P γ), γ<0 associated with the Euler equation for a two dimensional inviscid incompressible fluid which carries a pointwise flow φt (time evolution) leavingP γ globally invariant. φt is obtained as the limit of Galerkin approximations associated with Euler equations.P γ 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.
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Communicated by H. Araki
Dedication. After completion of this work the terrible news of the sudden death of Raphael Høgh-Krohn reached us. In deep sorrow we mourn his departure. The present work has its roots in previous inspiring work by him and we dedicate it to him as a small sign of our gratitude.
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Albeverio, S., Cruzeiro, AB. Global flows with invariant (Gibbs) measures for Euler and Navier-Stokes two dimensional fluids. Commun.Math. Phys. 129, 431–444 (1990). https://doi.org/10.1007/BF02097100
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DOI: https://doi.org/10.1007/BF02097100