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The Gibbs ensemble of a vortex filament. (English) Zbl 0992.60058
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.

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.)
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