Two-uniqueness of rational ghost soliton solution and well-posedness of perturbed Einstein-Yang-Mills equations

Wenjing Song; Haiyun Deng; Ganshan Yang; Wenjing Song; Haiyun Deng; Ganshan Yang

doi:10.3934/math.2021699

AIMS Mathematics

2021, Volume 6, Issue 11: 12065-12076. doi: 10.3934/math.2021699

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Research article

Two-uniqueness of rational ghost soliton solution and well-posedness of perturbed Einstein-Yang-Mills equations

1.
College of Science, Xi'an Polytechnic University, Xi'an, 710048, China
2.
Department of Applied Mathematics, Nanjing Audit University, Nanjing, 211815, China
3.
Department of Mathematics, Yunnan Nationalities University, Kunming, 650031, China

Received: 08 May 2021 Accepted: 12 August 2021 Published: 19 August 2021
MSC : 53C25, 53C26, 58J60

In this paper, we discuss the uniqueness and existence of local solutions for the perturbed static, spherically symmetric Einstein-Yang-Mills (EYM) equations with gauge group $ SU(2) $. Moreover, we show that the rational expression solutions to the equations only happened in traditional Schwarzschild solutions and Reissner-Nordstrom solutions. From these results, we can infer that there is no rational ghost soliton solution for the EYM equations.
- perturbed Einstein-Yang-Mills equations,
- rational expression solutions,
- $ C^{2+\alpha} $ solutions,
- well-posedness,
- ghost soliton
Citation: Wenjing Song, Haiyun Deng, Ganshan Yang. Two-uniqueness of rational ghost soliton solution and well-posedness of perturbed Einstein-Yang-Mills equations[J]. AIMS Mathematics, 2021, 6(11): 12065-12076. doi: 10.3934/math.2021699

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Abstract

In this paper, we discuss the uniqueness and existence of local solutions for the perturbed static, spherically symmetric Einstein-Yang-Mills (EYM) equations with gauge group $ SU(2) $. Moreover, we show that the rational expression solutions to the equations only happened in traditional Schwarzschild solutions and Reissner-Nordstrom solutions. From these results, we can infer that there is no rational ghost soliton solution for the EYM equations.

References

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