Well-posedness for the Chern-Simons-Schrödinger equations

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) $.

Keywords

• chern-simons-schrödinger
• coulomb gauge
• well-posedness