Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Construction of Multi-Bubble Solutions for a System of Elliptic
  Equations arising in Rank Two Gauge Theory   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 Liouville type. Under nearly necessary
conditions(see Theorem \ref{main-thm}), we show that there exist a sequence of
solutions $(u_{1,\varepsilon}, u_{2,\varepsilon})$ to \eqref{e051} such that
$u_{1,\varepsilon}$ and $u_{2,\varepsilon}$ blow up simultaneously at $k$
points in $\Omega$ as $\varepsilon\to 0$.

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The categories of this paper are: patt-sol
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The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
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The categories of this paper are: stat
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The categories of this paper are: eess
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The categories of this paper are: econ
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: hep-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: adap-org
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The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph