[1]周羽,金艳.(1+1)维Maxwell - Chern - Simons -Higgs系统解的整体存在性[J].延边大学学报(自然科学版),2023,(01):16-20.
　ZHOU Yu,JIN Yan.Global existence of Maxwell - Chern - Simons -Higgs system in(1+1)- dimension[J].Journal of Yanbian University,2023,(01):16-20.
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(1+1)维Maxwell - Chern - Simons -Higgs系统解的整体存在性

《延边大学学报(自然科学版)》[ISSN:1004-4353/CN:22-1191/N] 卷: 期数: 2023年01期 页码: 16-20 栏目: 基础科学研究 出版日期: 2023-02-01
Title:
Global existence of Maxwell - Chern - Simons -Higgs system in(1+1)- dimension
文章编号:
1004-4353(2023)01-0016-05
作者:
周羽;  金艳
(延边大学 理学院, 吉林 延吉 133002)
Author(s):
ZHOU Yu;  JIN Yan
(College of Science, Yanbian University, Yanji 133002, China)
关键词:
Maxwell - Chern - Simons -Higgs系统;  规范不变性;  降维模型;  整体解
Keywords:
Maxwell - Chern - Simons -Higgs system;  specification invariance;  reduced dimension model;  global solution
分类号:
O175.29
文献标志码:
A
摘要:
通过降维(1+2)维Maxwell - Chern - Simons -Higgs系统得到了(1+1)维Maxwell - Chern - Simons -Higgs系统,并在Lorenz规范条件下研究了(1+1)维Maxwell - Chern - Simons -Higgs系统解的整体存在性.应用Sobolev空间相关理论,证明了(1+1)维Maxwell - Chern - Simons -Higgs系统的解在H2×H1上具有整体存在性,同时还验证了该系统所对应的能量函数是守恒的.
Abstract:
The(1+1)- dimensional Maxwell - Chern - Simons -Higgs system is obtained by reducing the(1+2)- dimensional Maxwell - Chern - Simons -Higgs system, and the global existence of solutions of(1+1)- dimensional Maxwell - Chern - Simons -Higgs system is studied under Lorenz gauge condition.Applying the relevant theory of Sobolev space, it is proved that the solution of the(1+1)- dimensional Maxwell - Chern - Simons -Higgs system has global existence in H2×H1.Verfication indicate that the corresponding energy function of the system is conservative.

参考文献/References:

[1] LEE C, LEE K, MIN H.Self - dual Maxwell - Chern - Simons solitons [J].Phys Lett B, 1990,252:79 - 83.
[2] CHAE D, CHAE M.The global existence in the Cauchy problem of the Maxwell - Chern - Simons - Higgs system [J].J Math Phys, 2002,43:5470 - 5482.
[3] HUH H.Global energy solution of Chern - Simons - Higgs equations in one space dimension [J].J Math Anal Appl, 2014,420(1):781 - 791.
[4] JIN G, MOON B.Local and global solutions to the O(3)- sigma model with the Maxwell and the Chern - Simons gauges in R1+1 [J].J Math Anal Appl, 2021,495:124715.
[5] SOGGE C D.Lectures on nonlinear wave equations [M].Boston MA: International Press, 1995.
[6] GINIBRE J, VELO G.The Cauchy problem for coupled Yang - Mills and scalar fields in the temporal gauge [J].Comm Math Phys, 1981,82(1):1 - 28.
[7] HUH H.Cauchy problems of the gauged sigma model [J].J Math Phys, 2005,46(5):052303.
[8] YUAN J.Well - posedness of Maxwell - Chern - Simons - Higgs system in the Lorenz gauge [J].Discrete Contin Dyn Syst Ser A, 2014,34(5):2389 - 2403.
[9] CHERN S, SIMONS J.Characteristic forms and geometric invariants [J].Ann Math, 1974,99(1):48 - 69.
[10] WITTEN E.Quantum field theory and the jones polynomial [J].Comm Math Phys, 1989,121(3):351 - 399.
[11] HUH H, JIN G.Remarks on Chern - Simons gauged O(3)sigma model in one space dimension [J].J Math Phys, 2019,60:021508.
[12] HAN J, SONG K.Topological solutions of the self - dual equations for the generalized Maxwell - Chern - Simons - Higgs model [J].J Math Anal Appl, 2021,504:125327.

备注/Memo

收稿日期: 2022-10-09
第一作者: 周羽(1996—),女,硕士研究生,研究方向为偏微分方程.
通信作者: 金艳(1986—),女,硕士,助教,研究方向为金融数学.

更新日期/Last Update: 2023-02-01