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

Abstract

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.

References in corpus (1)

• The sphere covering inequality and its dual

Cited by in corpus (6)

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• Local uniqueness of $m$-bubbling sequences for the Gel'fand equation
• Non-degeneracy and uniqueness of solutions to singular mean field equations on bounded domains
• Local uniqueness and non-degeneracy of blow up solutions of mean field equations with singular data
• Existence results for a non-relativistic Chern-Simons model with purely mutual interaction
• Microcanonical phase transitions for the vortex system