Publications [#243857] of Jonathan C. Mattingly
- Mattingly, JC; Pardoux, É, Malliavin calculus for the stochastic 2D Navier-Stokes equation,
Communications on Pure and Applied Mathematics, vol. 59 no. 12
pp. 1742-1790, WILEY, ISSN 0010-3640 [math.PR/0407215], [doi]
(last updated on 2019/02/19)
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, strictly positive density with respect to Lebesgue measure. In particular, our conditions are viscosity independent. We are mainly interested in forcing that excites a very small number of modes. All of the results rely on proving the nondegeneracy of the infinite-dimensional Malliavin matrix. © 2006 Wiley Periodicals, Inc.