A special class of stationary flows for two-dimensional Euler equations: A statistical mechanics description
- Cite this article as:
- Caglioti, E., Lions, P.L., Marchioro, C. et al. Commun.Math. Phys. (1992) 143: 501. doi:10.1007/BF02099262
Moreover, we study the variational principles associated to Eq. (A.1) and prove thai, when β→−8π+, either ϱβ → δx0 (weakly in the sense of measures) wherex0 denotes and equilibrium point of a single point vortex in Λ, or ϱβ converges to a smooth solution of (A.1) for β=−8π. Examples of both possibilities are given, although we are not able to solve the alternative for a given Λ. Finally, we discuss a possible connection of the present analysis with the 2-D turbulence.