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• W2624406593 abstract "We consider the Chern-Simons gauge theory of rank $2$ such as $SU(3)$, $SO(5)$, and $G_2$ Chern-Simons model in $mathbb{R}^2$. There may exist three types of solutions in these theories, that is, topological, nontopological, and mixed type solutions. Among others, mixed type solutions can only exist in non-Abelian Chern-Simons models. We show the existence of mixed type solutions with an arbitrary configuration of vortex points which has been a long-standing open problem. To show it, as the first step, we need to find when a priori bound would fail. For the purpose, we shall find partially blowing up mixed type solutions by using different scalings for different components. Due to the different scalings, we should control the mass contribution from infinity which is one of the important parts in this paper." @default.
• W2624406593 created "2017-06-15" @default.
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• W2624406593 date "2017-09-01" @default.
• W2624406593 modified "2023-09-28" @default.
• W2624406593 title "Existence of mixed type solutions in the Chern–Simons gauge theory of rank two in <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML altimg=si1.gif overflow=scroll><mml:msup><mml:mrow><mml:mi mathvariant=double-struck>R</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:math>" @default.
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• W2624406593 doi "https://doi.org/10.1016/j.jfa.2017.05.012" @default.
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