Electron. J. Diff. Eqns., Vol. 2005(2005), No. 92, pp. 126.
Statistical mechanics of the
point vortex system with random
intensities on
Cassio Neri
Abstract:
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 1vortex distribution is a minimizer of
the free energy functional and is associated to (some) solutions
of the following nonlinear Poisson Equation:
where
.
Submitted March 3, 2005. Published August 24, 2005.
Math Subject Classifications: 76F55, 82B5.
Key Words: Statistical mechanics; Npoint vortex system; Onsager theory;
mean field equation.
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Cassio Neri
Instituto de Matemática
Universidade Federal do Rio de Janeiro
Caixa Postal 68530, CEP: 21945970, Rio de Janeiro, Brazil
email: cassio@labma.ufrj.br

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