Malliavin calculus for the stochastic 2D Navier-Stokes equation

Journal Article

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.

Full Text

Duke Authors

Cited Authors

  • Mattingly, JC; Pardoux, É

Published Date

  • 2006

Published In

Volume / Issue

  • 59 / 12

Start / End Page

  • 1742 - 1790

International Standard Serial Number (ISSN)

  • 0010-3640

Digital Object Identifier (DOI)

  • 10.1002/cpa.20136