Well-posedness for the Chern-Simons-Schrödinger equations

Jishan Fan; Tohru Ozawa; Jishan Fan; Tohru Ozawa

doi:10.3934/math.2022955

AIMS Mathematics

2022, Volume 7, Issue 9: 17349-17356. doi: 10.3934/math.2022955

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Well-posedness for the Chern-Simons-Schrödinger equations

Jishan Fan ¹,
Tohru Ozawa ^{2
,
,}

1.
Department of Applied Mathematics, Nanjing Forestry University, Nanjing 210037, China
2.
Department of Applied Physics, Waseda University, Tokyo, 169-8555, Japan

Received: 24 May 2022 Revised: 19 July 2022 Accepted: 19 July 2022 Published: 26 July 2022
MSC : 35B30, 35B65, 35Q55

First, we prove uniform-in-$ \epsilon $ regularity estimates of local strong solutions to the Chern-Simons-Schrödinger equations in $ \mathbb{R}^2 $. Here $ \epsilon $ is the dispersion coefficient. Then we prove the global well-posedness of strong solutions to the limit problem $ (\epsilon = 0) $.
- Chern-Simons-Schrödinger,
- Coulomb gauge,
- well-posedness
Citation: Jishan Fan, Tohru Ozawa. Well-posedness for the Chern-Simons-Schrödinger equations[J]. AIMS Mathematics, 2022, 7(9): 17349-17356. doi: 10.3934/math.2022955

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Abstract

First, we prove uniform-in-$ \epsilon $ regularity estimates of local strong solutions to the Chern-Simons-Schrödinger equations in $ \mathbb{R}^2 $. Here $ \epsilon $ is the dispersion coefficient. Then we prove the global well-posedness of strong solutions to the limit problem $ (\epsilon = 0) $.

References

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