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- W1566454909 abstract "In this paper we consider the following form of the so-called Mean field equation arising from the statistical mechanics description of two dimensional turbulence begin{equation}label{eq:study} - D_g u = rho_1 (frac{e^{u}}{int_Sig e^{u} dV_g}-1)-rho_2 (frac{e^{-u}}{int_Sig e^{-u} dV_g} - 1) end{equation} on a given closed orientable Riemannian surface ($Sigma, g$) with volume 1, where $rho_1, rho_2$ are real parameters. Exploiting the variational structure of the problem and running a min-max scheme introduced by Djadli and Malchiodi, we prove that if $k$ is a positive integer, $rho_1$ and $rho_2$ two real numbers such that $rho_1in (8kpi, 8(k+1)pi)$ and $rho_2<4pi$ then $eqref{eq:study}$ is solvable." @default.
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- W1566454909 date "2007-05-11" @default.
- W1566454909 modified "2023-09-27" @default.
- W1566454909 title "Existence results for mean field equations with turbulence" @default.
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