Blow up at infinity in the SU(3) Chern-Simons model, part I

Ting Jung Kuo; Youngae Lee; Chang Shou Lin

doi:10.1016/j.jfa.2020.108636

Blow up at infinity in the SU(3) Chern-Simons model, part I

Ting Jung Kuo, Youngae Lee^*, Chang Shou Lin

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

We consider non-topological solutions of a nonlinear elliptic system problem (see (1.4) below) derived from the SU(3) Chern-Simons models in R². The existence of non-topological solutions even for radial symmetric case has been a long standing open problem. Recently, Choe, Kim, and Lin in [7,8] showed the existence of radial symmetric non-topological solution when the vortex points collapse. However, the arguments in [7,8] cannot work for an arbitrary configuration of vortex points. In this paper, we develop a new approach by using different scalings for different components of the system to construct a family of non-topological solutions, which blows up at infinity.

Original language	English
Article number	108636
Journal	Journal of Functional Analysis
Volume	279
Issue number	7
DOIs	https://doi.org/10.1016/j.jfa.2020.108636
Publication status	Published - 2020 Oct 15

Keywords

Non-Abelian Chern-Simons models
Non-topological solutions
Partial blowing up solutions

ASJC Scopus subject areas

Analysis

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10.1016/j.jfa.2020.108636

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title = "Blow up at infinity in the SU(3) Chern-Simons model, part I",

abstract = "We consider non-topological solutions of a nonlinear elliptic system problem (see (1.4) below) derived from the SU(3) Chern-Simons models in R2. The existence of non-topological solutions even for radial symmetric case has been a long standing open problem. Recently, Choe, Kim, and Lin in [7,8] showed the existence of radial symmetric non-topological solution when the vortex points collapse. However, the arguments in [7,8] cannot work for an arbitrary configuration of vortex points. In this paper, we develop a new approach by using different scalings for different components of the system to construct a family of non-topological solutions, which blows up at infinity.",

keywords = "Non-Abelian Chern-Simons models, Non-topological solutions, Partial blowing up solutions",

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AU - Kuo, Ting Jung

AU - Lee, Youngae

AU - Lin, Chang Shou

PY - 2020/10/15

Y1 - 2020/10/15

N2 - We consider non-topological solutions of a nonlinear elliptic system problem (see (1.4) below) derived from the SU(3) Chern-Simons models in R2. The existence of non-topological solutions even for radial symmetric case has been a long standing open problem. Recently, Choe, Kim, and Lin in [7,8] showed the existence of radial symmetric non-topological solution when the vortex points collapse. However, the arguments in [7,8] cannot work for an arbitrary configuration of vortex points. In this paper, we develop a new approach by using different scalings for different components of the system to construct a family of non-topological solutions, which blows up at infinity.

AB - We consider non-topological solutions of a nonlinear elliptic system problem (see (1.4) below) derived from the SU(3) Chern-Simons models in R2. The existence of non-topological solutions even for radial symmetric case has been a long standing open problem. Recently, Choe, Kim, and Lin in [7,8] showed the existence of radial symmetric non-topological solution when the vortex points collapse. However, the arguments in [7,8] cannot work for an arbitrary configuration of vortex points. In this paper, we develop a new approach by using different scalings for different components of the system to construct a family of non-topological solutions, which blows up at infinity.

KW - Non-Abelian Chern-Simons models

KW - Non-topological solutions

KW - Partial blowing up solutions

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Blow up at infinity in the SU(3) Chern-Simons model, part I

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Keywords

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