On the Stochastic Navier–Stokes Equation Driven by Stationary White Noise

  • Chia Ying LeeEmail author
  • Boris Rozovskii
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 34)


We consider an unbiased approximation of stochastic Navier–Stokes equation driven by spatial white noise. This perturbation is unbiased in that the expectation of a solution of the perturbed equation solves the deterministic Navier–Stokes equation. The nonlinear term can be characterized as the highest stochastic order approximation of the original nonlinear term uu. We investigate the analytical properties and long-time behavior of the solution. The perturbed equation is solved in the space of generalized stochastic processes using the Cameron–Martin version of the Wiener chaos expansion and generalized Malliavin calculus. We also study the accuracy of the Galerkin approximation of the solutions of the unbiased stochastic Navier–Stokes equations.


Stokes Equation Steady Solution Catalan Number Propagator System Wick Product 
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B. L. Rozovskii acknowledges support from AFOSR MURI Grant 955-05-1-0613.


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© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Statistical and Applied Mathematical Sciences InstituteResearch Triangle ParkUSA
  2. 2.Division of Applied MathematicsBrown UniversityProvidenceUSA

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