Statistical mechanics of the N-point vortex system with random intensities on ℝ2
Files
Date
2005-08-24
Authors
Neri, Cassio
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University-San Marcos, Department of Mathematics
Abstract
The system of N-point vortices on ℝ2 is considered under the hypothesis that vortex intensities are independent and identically distributed random variables with respect to a law P supported on (0, 1]. It is shown that, in the limit as N approaches ∞, the 1-vortex distribution is a minimizer of the free energy functional and is associated to (some) solutions of the following non-linear Poisson Equation:
-∆u(x) = C-1 ∫(0, 1] re-βru(x)-γr|x|2 P(dr), ∀x ∈ ℝ2,
where C = ∫(0, 1] ∫ℝ2 e-βru(y) -γr|y|2 dyP(dr).
Description
Keywords
Statistical mechanics, N-point vortex system, Onsager theory, Mean field equation
Citation
Neri, C. (2005). Statistical mechanics of the N-point vortex system with random intensities on ℝ2. <i>Electronic Journal of Differential Equations, 2005</i>(92), pp. 1-26.
Rights
Attribution 4.0 International