Existence results for mean field equations with turbulence
| dc.creator | Ndiaye, Cheikh Birahim | |
| dc.date | 2007-05-11 | |
| dc.date.accessioned | 2026-07-07T08:00:59Z | |
| dc.date.available | 2026-07-07T08:00:59Z | |
| dc.description | 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 = ρ_1 (\frac{e^{u}}{\int_\Sig e^{u} dV_g}-1)-ρ_2 (\frac{e^{-u}}{\int_\Sig e^{-u} dV_g} - 1) \end{equation} on a given closed orientable Riemannian surface ($Σ, g$) with volume 1, where $ρ_1, ρ_2$ 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, $ρ_1$ and $ρ_2$ two real numbers such that $ρ_1\in (8kπ, 8(k+1)π)$ and $ρ_2<4π$ then $\eqref{eq:study}$ is solvable. | |
| dc.identifier | https://arxiv.org/abs/0705.1687 | |
| dc.identifier | http://arxiv.org/abs/0705.1687 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/128815 | |
| dc.subject | Analysis of PDEs | |
| dc.title | Existence results for mean field equations with turbulence | |
| dc.type | text |