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

Franco Flandoli; Marco Romito

Mathematica Bohemica (2002)

  • Volume: 127, Issue: 2, page 211-218
  • ISSN: 0862-7959

Abstract

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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.

How to cite

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Flandoli, Franco, and Romito, Marco. "Probabilistic analysis of singularities for the 3D Navier-Stokes equations." Mathematica Bohemica 127.2 (2002): 211-218. <http://eudml.org/doc/249057>.

@article{Flandoli2002,
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.},
author = {Flandoli, Franco, Romito, Marco},
journal = {Mathematica Bohemica},
keywords = {singularities; Navier-Stokes equations; Brownian motion; stationary solutions; singularities; Navier-Stokes equations; Brownian motion; stationary solutions},
language = {eng},
number = {2},
pages = {211-218},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Probabilistic analysis of singularities for the 3D Navier-Stokes equations},
url = {http://eudml.org/doc/249057},
volume = {127},
year = {2002},
}

TY - JOUR
AU - Flandoli, Franco
AU - Romito, Marco
TI - Probabilistic analysis of singularities for the 3D Navier-Stokes equations
JO - Mathematica Bohemica
PY - 2002
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 127
IS - 2
SP - 211
EP - 218
AB - 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.
LA - eng
KW - singularities; Navier-Stokes equations; Brownian motion; stationary solutions; singularities; Navier-Stokes equations; Brownian motion; stationary solutions
UR - http://eudml.org/doc/249057
ER -

References

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