Browsing by Author "Pardoux, E"

Now showing 1 - 1 of 1
  • Thumbnail Image
    ItemOpen Access
    Malliavin calculus for the stochastic 2D Navier-Stokes equation
    (Communications on Pure and Applied Mathematics, 2006-12-01) Mattingly, JC; Pardoux, E
    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.