On Unbiased Perturbations of Navier-Stokes Equations

Boris Rozovsky
Brown University

A new class of stochastic perturbations of Navier-Stokes equation wil be discussed.
A unique feature of this type of perturbation is that it preserves the mean dynamics:
the expectation of the solution of the perturbation solves the underlying deterministic
Navier-Stokes equation. From the stand point of a statistician it means that the
perturbed model is an unbiased random perturbation of the deterministic Navier-
Stokes equation. Space-time and stationary solutions will be considered as well as
the convergence of space-time solutions to stationary solutions as t ! 1: It will
be shown that a solution of the unbiased perturbation is unique if and only if the
uniqueness property holds for the underlying deterministic Navier-Stokes equation.
Some numerical features of the unbiased perturbations will be discussed.
The talk is based on joint papers with R. Mikulevicius and C. Y. Lee.

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