Blowup behavior for a degenerate elliptic sinh-Poisson equation with variable intensities

Abstract

In this paper, we provide a complete blow-up picture for solution sequences to an elliptic sinh-Poisson equation with variable intensities arising in the context of the statistical mechanics description of two-dimensional turbulence, as initiated by Onsager. The vortex intensities are described in terms of a probability measure defined on the interval. Under Dirichlet boundary conditions we establish the exclusion of boundary blowup points, we show that the concentration mass does not have residual L1-terms and we determine the location of blowup points in terms of Kirchhoff's Hamiltonian. We allow the measure to be a general Borel measure, which could be "degenerate." Our main results are new for the standard sinh-Poisson equation as well.

References in corpus (3)

• Elliptic Equations Involving Meausres
• Extremal boundedness of a variational functional in point vortex mean field theory associated with probability measures
• Mass quantization and minimax solutions for Neri's mean field equation in 2D-turbulence

Cited by in corpus (4)

• Blow-up analysis and existence results in the supercritical case for an asymmetric mean field equation with variable intensities
• On the existence and blow-up of solutions for a mean field equation with variable intensities
• On the Topological degree of the Mean field equation with two parameters
• A mean field equation involving positively supported probability measures: blow-up phenomena and variational aspects