Flandoli, Franco; Gubinelli, Massimiliano The Gibbs ensemble of a vortex filament. (English) Zbl 0992.60058 Probab. Theory Relat. Fields 122, No. 3, 317-340 (2002). Summary: We introduce a statistical ensemble for a single vortex filament of a three-dimensional incompressible fluid. The core of the vortex is modeled by a quite generic stochastic process. We prove the existence of the partition function for both positive and a limited range of negative temperatures. Cited in 13 Documents MSC: 60H05 Stochastic integrals 76F05 Isotropic turbulence; homogeneous turbulence 76M23 Vortex methods applied to problems in fluid mechanics 82B99 Equilibrium statistical mechanics 60H30 Applications of stochastic analysis (to PDEs, etc.) Keywords:single vortex filament; three-dimensional incompressible fluid PDF BibTeX XML Cite \textit{F. Flandoli} and \textit{M. Gubinelli}, Probab. Theory Relat. Fields 122, No. 3, 317--340 (2002; Zbl 0992.60058) Full Text: DOI