Math @ Duke

Publications [#243857] of Jonathan C. Mattingly
Papers Published
 Mattingly, JC; Pardoux, É, Malliavin calculus for the stochastic 2D NavierStokes equation,
Communications on Pure & Applied Mathematics, vol. 59 no. 12
(December, 2006),
pp. 17421790, ISSN 00103640 [math.PR/0407215], [doi]
(last updated on 2017/12/18)
Abstract: We consider the incompressible, twodimensional NavierStokes equation with periodic boundary conditions under the effect of an additive, whiteintime, stochastic forcing. Under mild restrictions on the geometry of the scales forced, we show that any finitedimensional 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 infinitedimensional Malliavin matrix. © 2006 Wiley Periodicals, Inc.


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