Statistical mechanics of the N-point vortex system with random intensities on ℝ2
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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).
CitationNeri, C. (2005). Statistical mechanics of the N-point vortex system with random intensities on ℝ2. Electronic Journal of Differential Equations, 2005(92), pp. 1-26.
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