| Title:
|
Probabilistic analysis of singularities for the 3D Navier-Stokes equations (English) |
| Author:
|
Flandoli, Franco |
| Author:
|
Romito, Marco |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
127 |
| Issue:
|
2 |
| Year:
|
2002 |
| Pages:
|
211-218 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
singularities |
| Keyword:
|
Navier-Stokes equations |
| Keyword:
|
Brownian motion |
| Keyword:
|
stationary solutions |
| MSC:
|
35Q30 |
| MSC:
|
60H15 |
| MSC:
|
76D05 |
| MSC:
|
76D06 |
| MSC:
|
76M35 |
| idZBL:
|
Zbl 1137.76353 |
| idMR:
|
MR1981526 |
| DOI:
|
10.21136/MB.2002.134166 |
| . |
| Date available:
|
2012-10-05T12:55:55Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134166 |
| . |
| Reference:
|
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| . |
