dc.contributor.author Neri, Cassio ( 0000-0001-6940-188X ) dc.date.accessioned 2021-06-01T15:21:42Z dc.date.available 2021-06-01T15:21:42Z dc.date.issued 2005-08-24 dc.identifier.citation Neri, 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 dc.identifier.issn 1072-6691 dc.identifier.uri https://digital.library.txstate.edu/handle/10877/13693 dc.description.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).``` dc.format Text dc.format.extent 26 pages dc.format.medium 1 file (.pdf) dc.language.iso en en_US dc.publisher Texas State University-San Marcos, Department of Mathematics en_US dc.source Electronic Journal of Differential Equations, 2005, San Marcos, Texas: Texas State University-San Marcos and University of North Texas. dc.subject Statistical mechanics en_US dc.subject N-point vortex system en_US dc.subject Onsager theory en_US dc.subject Mean field equation en_US dc.title Statistical mechanics of the N-point vortex system with random intensities on ℝ2 en_US dc.type publishedVersion txstate.documenttype Article dc.rights.license This work is licensed under a Creative Commons Attribution 4.0 International License.
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