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.
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Received: 31 July 2000 / Revised version: 6 March 2001 / Published online: 20 December 2001
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Flandoli, F., Gubinelli, M. The Gibbs ensemble of a vortex filament. Probab Theory Relat Fields 122, 317–340 (2002). https://doi.org/10.1007/s004400100163
- Stochastic Process
- Partition Function
- Limited Range
- Incompressible Fluid