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Global flows with invariant (Gibbs) measures for Euler and Navier-Stokes two dimensional fluids. (English) Zbl 0702.76041

Summary: We construct a family of probability spaces (\(\Omega\),\({\mathcal F},P_{\gamma})\), \(\gamma >0\) associated with the Euler equation for a two-dimensional inviscid incompressible fluid which carries a pointwise flow \(\phi_ t\) (time evolution) leaving \(P_{\gamma}\) globally invariant. \(\phi_ t\) is obtained as the limit of Galerkin approximations associated with Euler equations. \(P_{\gamma}\) is also an invariant measure for a stochastic process associated with a Navier- Stokes equation with viscosity \(\gamma\), stochastically perturbed by a white noise force.

MSC:

76D05 Navier-Stokes equations for incompressible viscous fluids
35Q30 Navier-Stokes equations
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