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.
Probabilistic analysis of singularities for the 3D Navier-Stokes equations / F. FLANDOLI; M. ROMITO. - In: MATHEMATICA BOHEMICA. - ISSN 0862-7959. - STAMPA. - 127 (no. 2):(2002), pp. 211-218. (Intervento presentato al convegno Equadiff 10 tenutosi a Praga nel August 27–31, 2001).
Probabilistic analysis of singularities for the 3D Navier-Stokes equations
ROMITO, MARCO
2002
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.
I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
