Uniqueness of solutions of the stochastic Navier-Stokes equation with invariant measure given by the enstrophy

• 成果类型: Article
• 署名作者: Albeverio, S; Ferrario, B
• 署名单位: University of Bonn; University of Pavia
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117904000000379
• 发表日期: 2004
• 页码: 1632-1649
• 关键词: 2-dimensional euler; FLOWS

摘要

A stochastic Navier-Stokes equation with space-time Gaussian white noise is considered, having as infinitesimal invariant measure a Gaussian measure mu(v) whose covariance is given in terms of the enstrophy. Pathwise uniqueness for mu(v)-a.e. initial velocity is proven for solutions having mu(v) as invariant measure.