2015/07/06 by Tonia Ricciardi, Ryo Takahashi, Ricciardi, Tonia +1
Mathematics · Computer Science · Economics, Econometrics and Finance · #Nonlinear Partial Differential Equations #Advanced Mathematical Modeling in Engineering #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1507.01449
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.