In this article, we consider the initial value problem for the Chern–Simons–Schrödinger model in two space dimensions. This is a covariant NLS type problem which is L2 critical. For this equation, we introduce a so-called heat gauge, and prove that, with respect to this gauge, the problem is locally well-posed for initial data which is small in Hs, s>0.
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Liu et al. (2013) studied this question.
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