Negative temperature bounds for 2D vorticity compounds

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


If λ ≥ 0 and Λ ⊂ ℝ2 is a connected Lipschitz domain, with |Λ| < ∞, it is a matter of standard convex functional analysis to show that the nonlinear eigenvalue problem of Poisson-Boltzmann type {Mathematical expression} with 0-Dirichlet boundary data for ψ, has a unique solution ψ0 Ξ 0. Here, we prove the stronger result that ψ =ψ0 Ξ 0 is the unique solution also for λ ∈ (λ*, 0), where λ* < 0 is some critical value which depends only on Λ, but in any event with λ* < -8 π/5. This result settles a conjecture about negative temperatures of vorticity compounds in 2D turbulence which goes back to 1949 work of Onsager.

Original languageAmerican English
Pages (from-to)49-57
Number of pages9
JournalLetters in Mathematical Physics
Issue number1
StatePublished - May 1995

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


  • Mathematical Subject Classifications (1991): 35Q53, 53A10, 76C05, 82D50


Dive into the research topics of 'Negative temperature bounds for 2D vorticity compounds'. Together they form a unique fingerprint.

Cite this