Blow-up analysis for some mean field equations involving probability measures from statistical hydrodynamics
Analysis of PDEs
2011-09-26 v1
Abstract
Motivated by the mean field equations with probability measure derived by Sawada-Suzuki and by Neri in the context of the statistical mechanics description of two-dimensional turbulence, we study the semilinear elliptic equation with probability measure: {equation*} -\Delta v=\lambda\int_I V(\alpha,x,v)e^{\alpha v}\,\Pda -\frac{\lambda}{|\Omega|}\iint_{I\times\Om}V(\alpha,x,v)e^{\alpha v}\,\Pda dx, {equation*} defined on a compact Riemannian surface. This equation includes the above mentioned equations of physical interest as special cases. For such an equation we study the blow-up properties of solution sequences. The optimal Trudinger-Moser inequality is also considered.
Keywords
Cite
@article{arxiv.1109.5001,
title = {Blow-up analysis for some mean field equations involving probability measures from statistical hydrodynamics},
author = {Tonia Ricciardi and Gabriella Zecca},
journal= {arXiv preprint arXiv:1109.5001},
year = {2011}
}