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.
Keywords
Cite
@article{arxiv.1507.01449,
title = {Blowup behavior for a degenerate elliptic sinh-Poisson equation with variable intensities},
author = {Tonia Ricciardi and Ryo Takahashi},
journal= {arXiv preprint arXiv:1507.01449},
year = {2015}
}