Calculus of Variations and Geometric Measure Theory

D. Bartolucci - A. Jevnikar - Y. Lee - W. Yang

Non degeneracy, Mean Field Equations and the Onsager theory of 2D turbulence

created by jevnikar on 28 Nov 2017
modified on 20 Mar 2018


Accepted Paper

Inserted: 28 nov 2017
Last Updated: 20 mar 2018

Journal: Arch. Rat. Mech. Anal.
Year: 2017


The understanding of some large energy, negative specific heat states in the Onsager description of 2D turbulence, seems to require the analysis of a subtle open problem about bubbling solutions of the mean field equation. Motivated by this application we prove that, under suitable non degeneracy assumptions on the associated $m$-vortex Hamiltonian, the $m$-point bubbling solutions of the mean field equation are non degenerate as well. Then we deduce that the Onsager mean field equilibrium entropy is smooth and strictly convex in the high energy regime on domains of second kind.

Keywords: Mean field equations, Non degeneracy, Negative specific heat states