Archive for Rational Mechanics and Analysis

, Volume 230, Issue 1, pp 397–426 | Cite as

Non-degeneracy, Mean Field Equations and the Onsager Theory of 2D Turbulence

  • Daniele Bartolucci
  • Aleks Jevnikar
  • Youngae Lee
  • Wen Yang


The understanding of some large energy, negative specific heat states in the Onsager description of 2D turbulence seem 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.


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© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Rome “Tor Vergata”RomaItaly
  2. 2.Department of Mathematics Education, Teachers CollegeKyungpook National UniversityDaeguSouth Korea
  3. 3.Wuhan Institute of Physics and Mathematics, Chinese Academy of SciencesWuhanPeople’s Republic of China

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