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

Tonia Ricciardi; Ryo Takahashi

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arXiv · 1507.01449

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

Tonia Ricciardi·Ryo Takahashi

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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.

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Tonia Ricciardi, Ryo Takahashi. 2015-07-06. Blowup behavior for a degenerate elliptic sinh-Poisson equation with variable intensities. https://arxiv.org/abs/1507.01449

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