Global L2-solutions of stochastic Navier-Stokes equations

• 成果类型: Article
• 署名作者: Mikulevicius, R; Rozovskii, BL
• 署名单位: University of Southern California; University of Southern California
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117904000000630
• 发表日期: 2005
• 页码: 137-176
• 关键词: Existence; SPACE

摘要

This paper concerns the Cauchy problem in R-d for the stochastic Navier-Stokes equation partial derivativetu = Deltau - (u, del)u - delp + f(u) + [(sigma, del)u - delp + g(u)] o W, u(0) = u(0), div u = 0, driven by white noise W. Under minimal assumptions on regularity of the coefficients and random forces, the existence of a global weak (martingale) solution of the stochastic Navier-Stokes equation is proved. In the two-dimensional case, the existence and pathwise uniqueness of a global strong solution is shown. A Wiener chaos-based criterion for the existence and uniqueness of a strong global solution of the Navier-Stokes equations is established.