Unbiased Random Perturbations of Navier-Stokes Equation

Unbiased Random Perturbations of Navier-Stokes Equation

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Boris Rozovsky, Lefschetz Center for Dynamical Systems, Brown University
Fine Hall 401

A random perturbation of a deterministic Navier-Stokes equation is considered in the form of an Stochastic PDE with Wick product in the nonlinear term. The equation is solved in the space of generalized stochastic processes using the Cameron-Martin version of the Wiener chaos expansion. The generalized solution is obtained as an inverse of solutions to corresponding quantized equations.An interesting feature of this type of perturbation is that it preserves the mean dynamics: the expectation of the solution of the perturbed equation solves the underlying deterministic Navier-Stokes equation. From the standpoint of a statistician it means that the perturbed model is unbiased. The talk is based on a joint work with R. Mikulevicius.