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dc.contributor.authorNeri, Cassio ( Orcid Icon 0000-0001-6940-188X )
dc.identifier.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.en_US

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).
dc.format.extent26 pages
dc.format.medium1 file (.pdf)
dc.publisherTexas State University-San Marcos, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2005, San Marcos, Texas: Texas State University-San Marcos and University of North Texas.
dc.subjectStatistical mechanicsen_US
dc.subjectN-point vortex systemen_US
dc.subjectOnsager theoryen_US
dc.subjectMean field equationen_US
dc.titleStatistical mechanics of the N-point vortex system with random intensities on ℝ2en_US
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.



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