Displaying similar documents to “Some results on invariant measures in hydrodynamics”

Probabilistic analysis of singularities for the 3D Navier-Stokes equations

Franco Flandoli, Marco Romito (2002)

Mathematica Bohemica

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The classical result on singularities for the 3D Navier-Stokes equations says that the 1 -dimensional Hausdorff measure of the set of singular points is zero. For a stochastic version of the equation, new results are proved. For statistically stationary solutions, at any given time t , with probability one the set of singular points is empty. The same result is true for a.e. initial condition with respect to a measure related to the stationary solution, and if the noise is sufficiently...