{"paper":{"title":"Construction of Multi-Bubble Solutions for a System of Elliptic Equations arising in Rank Two Gauge Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hsin-Yuan Huang","submitted_at":"2018-11-15T16:54:58Z","abstract_excerpt":"We study the existence of multi-bubble solutions for the following skew-symmetric Chern--Simons system \\begin{equation}\\label{e051} \\left\\{ \\begin{split} &\\Delta u_1+\\frac{1}{\\varepsilon^2}e^{u_2}(1-e^{u_1})=4\\pi\\sum_{i=1}^{2k}\\delta_{p_{1,i}}\\\\ &\\Delta u_2+\\frac{1}{\\varepsilon^2}e^{u_1}(1-e^{u_2})=4\\pi\\sum_{i=1}^{2k}\\delta_{p_{2,i}} \\end{split} \\text{ in }\\quad \\Omega\\right., \\end{equation} where $k\\geq 1$ and $\\Omega$ is a flat tours in $\\mathbb{R}^2$. It continues the joint work with Zhang\\cite{HZ-2015}, where we obtained the necessary conditions for the existence of bubbling solutions of L"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.06463","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}