Low regularity solutions to the non-abelian Chern–Simons–Higgs system in the Lorenz gauge

Yonggeun Cho; Seokchang Hong

doi:10.1007/s00030-021-00732-5

Low regularity solutions to the non-abelian Chern–Simons–Higgs system in the Lorenz gauge

Yonggeun Cho
, Seokchang Hong^*

^*Corresponding author for this work

Department of Mathematics

Seoul National University

Research output: Contribution to journal › Journal article › peer-review

1 Scopus citations

Abstract

In this paper we consider a Cauchy problem on the self-dual relativistic non-abelian Chern–Simons–Higgs model, which is the system of equations of sl(n,C)(n≥2)-valued matter field ϕ and gauge field A. Based on the frequency localization as well as the null structure we show local well-posedness in the Sobolev space Hs+12×Hs for s>14. We also prove that the solution flow map (ϕ(0) , A(0)) ↦ (ϕ(t) , A(t)) fails to be C² at the origin of H^s× H^σ when σ< max (0 , s- 1) regardless of s∈ R.

Original language	English
Article number	70
Journal	Nonlinear Differential Equations and Applications
Volume	28
Issue number	6
DOIs	https://doi.org/10.1007/s00030-021-00732-5
State	Published - 2021.12

Keywords

Bilinear estimates
Chern–Simons–Higgs system
Failure of C smoothness
Local well-posedness
Non-abelian gauge theory
Null structure

Quacquarelli Symonds(QS) Subject Topics

Mathematics

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10.1007/s00030-021-00732-5

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@article{9048b2df08df48f0960c452fdd417237,

title = "Low regularity solutions to the non-abelian Chern–Simons–Higgs system in the Lorenz gauge",

abstract = "In this paper we consider a Cauchy problem on the self-dual relativistic non-abelian Chern–Simons–Higgs model, which is the system of equations of sl(n,C)(n≥2)-valued matter field ϕ and gauge field A. Based on the frequency localization as well as the null structure we show local well-posedness in the Sobolev space Hs+12×Hs for s>14. We also prove that the solution flow map (ϕ(0) , A(0)) ↦ (ϕ(t) , A(t)) fails to be C2 at the origin of Hs× Hσ when σ< max (0 , s- 1) regardless of s∈ R.",

keywords = "Bilinear estimates, Chern–Simons–Higgs system, Failure of C smoothness, Local well-posedness, Non-abelian gauge theory, Null structure",

author = "Yonggeun Cho and Seokchang Hong",

note = "Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG.",

year = "2021",

month = dec,

doi = "10.1007/s00030-021-00732-5",

language = "English",

volume = "28",

journal = "Nonlinear Differential Equations and Applications",

issn = "1021-9722",

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TY - JOUR

T1 - Low regularity solutions to the non-abelian Chern–Simons–Higgs system in the Lorenz gauge

AU - Cho, Yonggeun

AU - Hong, Seokchang

PY - 2021/12

Y1 - 2021/12

N2 - In this paper we consider a Cauchy problem on the self-dual relativistic non-abelian Chern–Simons–Higgs model, which is the system of equations of sl(n,C)(n≥2)-valued matter field ϕ and gauge field A. Based on the frequency localization as well as the null structure we show local well-posedness in the Sobolev space Hs+12×Hs for s>14. We also prove that the solution flow map (ϕ(0) , A(0)) ↦ (ϕ(t) , A(t)) fails to be C2 at the origin of Hs× Hσ when σ< max (0 , s- 1) regardless of s∈ R.

AB - In this paper we consider a Cauchy problem on the self-dual relativistic non-abelian Chern–Simons–Higgs model, which is the system of equations of sl(n,C)(n≥2)-valued matter field ϕ and gauge field A. Based on the frequency localization as well as the null structure we show local well-posedness in the Sobolev space Hs+12×Hs for s>14. We also prove that the solution flow map (ϕ(0) , A(0)) ↦ (ϕ(t) , A(t)) fails to be C2 at the origin of Hs× Hσ when σ< max (0 , s- 1) regardless of s∈ R.

KW - Bilinear estimates

KW - Chern–Simons–Higgs system

KW - Failure of C smoothness

KW - Local well-posedness

KW - Non-abelian gauge theory

KW - Null structure

UR - https://www.scopus.com/pages/publications/85117321063

U2 - 10.1007/s00030-021-00732-5

DO - 10.1007/s00030-021-00732-5

M3 - Journal article

AN - SCOPUS:85117321063

SN - 1021-9722

VL - 28

JO - Nonlinear Differential Equations and Applications

JF - Nonlinear Differential Equations and Applications

IS - 6

M1 - 70

ER -

Low regularity solutions to the non-abelian Chern–Simons–Higgs system in the Lorenz gauge

Abstract

Keywords

Quacquarelli Symonds(QS) Subject Topics

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