We prove that the Chern-Simons-Schrdinger system, under the condition of a Coulomb gauge, has a unique local-in-time solution in the energy space 1 (R 2 ). The Coulomb gauge provides elliptic features for gauge fields 0 , . The Koch-and Tzvetkov-type Strichartz estimate is applied with Hardy-Littlewood-Sobolev and Wente's inequalities.
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Hyungjin Huh (2013) studied this question.
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