A stochastic representation for backward incompressible Navier-Stokes equations

• 成果类型: Article
• 署名作者: Zhang, Xicheng
• 署名单位: Huazhong University of Science & Technology; University of New South Wales Sydney
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-009-0234-6
• 发表日期: 2010
• 页码: 305-332
• 关键词: flows

摘要

By reversing the time variable we derive a stochastic representation for backward incompressible Navier-Stokes equations in terms of stochastic Lagrangian paths, which is similar to Constantin and Iyer's forward formulations in Constantin and Iyer (Comm Pure Appl Math LXI:330-345, 2008). Using this representation, a self-contained proof of local existence of solutions in Sobolev spaces are provided for incompressible Navier-Stokes equations in the whole space. In two dimensions or large viscosity, an alternative proof to the global existence is also given. Moreover, a large deviation estimate for stochastic particle trajectories is presented when the viscosity tends to zero.