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Existence and asymptotic behavior of solutions to the Abelian Higgs model with impurity

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Abstract

We study the static Abelian Higgs model with impurity subject to external fields on \(\mathbb {R}^{3}\). The existence and regularity of the solutions are established under the condition that the gauge fields satisfy the Coulomb gauge. The boundedness of the order parameters and the asymptotic behavior of the solutions at the infinity are also obtained.

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Acknowledgements

This work was supported in part by the National Natural Science Foundation of China under Grants 11471099 and 11671120.

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Authors and Affiliations

  1. Henan University, Kaifeng, 475001, People’s Republic of China

    Ruifeng Zhang

  2. College of Mathematics and Information Science, Henan University, Kaifeng, 475001, People’s Republic of China

    Ruifeng Zhang & Yaru Liang

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  1. Ruifeng Zhang
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  2. Yaru Liang
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Correspondence to Ruifeng Zhang.

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Zhang, R., Liang, Y. Existence and asymptotic behavior of solutions to the Abelian Higgs model with impurity. Z. Angew. Math. Phys. 70, 12 (2019). https://doi.org/10.1007/s00033-018-1054-2

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  • DOI: https://doi.org/10.1007/s00033-018-1054-2

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