On Stochastic Navier-Stokes Equation Driven by Stationary White Noise
نویسندگان
چکیده
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 u∇u. 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.
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