On unbiased stochastic Navier-Stokes equations

• 成果类型: Article
• 署名作者: Mikulevicius, R.; Rozovskii, B. L.
• 署名单位: Brown University; University of Southern California
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-011-0384-1
• 发表日期: 2012
• 页码: 787-834
• 关键词: driven

摘要

A random perturbation of a deterministic Navier-Stokes equation is considered in the form of an SPDE with Wick type nonlinearity. The nonlinear term of the perturbation can be characterized as the highest stochastic order approximation of the original nonlinear term . This perturbation is unbiased in that the expectation of a solution of the perturbed equation solves the deterministic Navier-Stokes equation. The perturbed equation is solved in the space of generalized stochastic processes using the Cameron-Martin version of the Wiener chaos expansion. It is shown that the generalized solution is a Markov process and scales effectively by Catalan numbers.