The system of N -point vortices on is considered under the hypothesis that vortex intensities are independent and identically distributed random variables with respect to a law supported on . It is shown that, in the limit as 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:
Submitted March 3, 2005. Published August 24, 2005.
Math Subject Classifications: 76F55, 82B5.
Key Words: Statistical mechanics; N-point vortex system; Onsager theory; mean field equation.
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| Cassio Neri |
Instituto de Matemática
Universidade Federal do Rio de Janeiro
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