Math @ Duke
|
Publications [#49711] of Jonathan C. Mattingly
search arxiv.org.Papers Published
- Jonathan C. Mattingly, Etienne Pardoux, Malliavin calculus for the Stochastic 2D Navier Stokes Equation,
Communications on Pure and Applied Mathematics, vol. 59 no. 12
(December, 2006),
pp. 1742 - 1790 [math.PR/0407215]
(last updated on 2007/03/21)
Abstract: We consider the incompressible, two
dimensional Navier Stokes equation with
periodic boundary conditions under the effect
of an additive, white in time,
stochastic forcing. Under mild restrictions
on the geometry of the scales
forced, we show that any finite dimensional
projection of the solution
possesses a smooth density with respect to
Lebesgue measure. We also show that
under natural assumptions the density of such
a projection is everywhere
strictly positive. In particular, our
conditions are viscosity independent. We
are mainly interested in forcing which
excites a very small number of modes.
All of the results rely on the nondegeneracy
of the infinite dimensional
Malliavin matrix.
|
|
dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821
| |
Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320
|
|