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Research Article | Open Access

Well-posedness for the Chern-Simons-Schrödinger equations

Jishan Fan1, Tohru Ozawa2( )
Department of Applied Mathematics, Nanjing Forestry University, Nanjing 210037, China
Department of Applied Physics, Waseda University, Tokyo, 169-8555, Japan
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Abstract

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

Keywords

Chern-Simons-SchrödingerCoulomb gaugewell-posedness
CLC number: 35B30, 35B65, 35Q55

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AIMS Mathematics
Volume 7 Issue 9,
September 2022
Pages 17349-17356
DOI: 10.3934/math.2022955

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Cite this article:
Fan J, Ozawa T. Well-posedness for the Chern-Simons-Schrödinger equations. AIMS Mathematics, 2022, 7(9): 17349-17356. https://doi.org/10.3934/math.2022955

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Received: 24 May 2022
Revised: 19 July 2022
Accepted: 19 July 2022
Published: 15 September 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)