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Well-posedness for the Chern-Simons-Schrödinger equations

  • 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) $.

    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

    Related Papers:

  • 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) $.



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