Geodesic
Probabilistic analysis of singularities for the 3D Navier-Stokes equations
Mathematica Bohemica, Tome 127 (2002) no. 2, pp. 211-218.

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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 non degenerate the support of such measure is the full energy space.
DOI : 10.21136/MB.2002.134166
Classification : 35Q30, 60H15, 76D05, 76D06, 76M35
Keywords: singularities; Navier-Stokes equations; Brownian motion; stationary solutions 
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Flandoli, Franco; Romito, Marco. Probabilistic analysis of singularities for the 3D Navier-Stokes equations. Mathematica Bohemica, Tome 127 (2002) no. 2, pp. 211-218. doi : 10.21136/MB.2002.134166. http://geodesic.mathdoc.fr/articles/10.21136/MB.2002.134166/

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