Franco Flandoli, Dipartimento di Matematica Applicata, Universita di Pisa, Via Bonanno 25/b, 56126 Pisa, Italy, e-mail: flandoli@dma.unipi.it; Marco Romito, Dipartimento di Matematica, Universita di Firenze, Viale Morgagni 67/a, 50134 Firenze, Italy, e-mail: romito@math.unifi.it
Abstract: 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.
Keywords: singularities, Navier-Stokes equations, Brownian motion, stationary solutions
Classification (MSC 2000): 76D06, 35Q30, 60H15
Full text available as PDF (smallest), as compressed PostScript (.ps.gz) or as raw PostScript (.ps).
Access to the full text of journal articles on this site is restricted to the subscribers of Myris Trade. To activate your access, please contact Myris Trade at myris@myris.cz.
