Profile of Blow-up Solutions to Mean Field Equations with Singular Data

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Some existence results for the Toda system on closed surfaces (2007, background): “arises in the study of mean field limit of point vortices of Euler flows, spherical Onsager vortex theory and condensates in some Chern-Simons-Higgs models, see for example the papers [3], [ 4 ], [7], [8], [9], [10], [12], [20], [30] and the references therein.”
Analytic aspects of the Toda system: II. Bubbling behavior and existence of solutions (2005, methodology): “A result given in [23] (see also [ 2 ]) gives that”
Compactness of solutions to the Yamabe problem (2004, unknown): “Analogous results, extensions, as well as different proofs of (12) can be found in [87], [90], [81], [22], [21], [74], [34], [33], [68], [16], [17], [36], [69], [64], [14], [78], [37], [65], [ 15 ], [88], [89], and others.”
Profile of bubbling solutions to a Liouville system (2009, background): “The results of Li[21] and Bartolucci, Chen, Lin, Tarantello [3] have been improved by Chen and Lin [9] and Zhang [29,30] to a sharper form.”
Classification of blowup limits for SU(3) singular Toda systems (2013, methodology): “These estimates were first obtained by Li [1999] for the scalar Liouville equation without singularity (using the method of moving planes) and [Bartolucci et al. 2004] for the scalar Liouville equation with singularity (using the Pohozaev identity and potential analysis).”