The evolution of a random vortex filament

• 成果类型: Article
• 署名作者: Bessaih, H; Gubinelli, M; Russo, F
• 署名单位: University of Wyoming; Universite Paris 13
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117905000000323
• 发表日期: 2005
• 页码: 1825-1855
• 关键词: probabilistic models; stochastic-analysis; ito formula; rough path; covariation; calculus

摘要

We study an evolution problem in the space of continuous loops in a three-dimensional Euclidean space modeled upon the dynamics of vortex lines in 3d incompressible and inviscid fluids. We establish existence of a local solution starting from Holder regular loops with index greater than 1/3. When the Holder regularity of the initial condition X is smaller or equal to 1/2, we require X to be a rough path in the sense of Lyons [Rev. Mat. Iberoamericana 14 (1998) 215-310, System Control and Rough Paths (2002). Oxford Univ. Press]. The solution will then live in an appropriate space of rough paths. In particular, we can construct (local) solution starting from almost every Brownian loop.