We prove that the Chern-Simons-Schrödinger system, under the condition of a Coulomb gauge, has a unique local-in-time solution in the energy space . The Coulomb gauge provides elliptic features for gauge fields . The Koch- and Tzvetkov-type Strichartz estimate is applied with Hardy-Littlewood-Sobolev and Wente's inequalities.
"Energy Solution to the Chern-Simons-Schrödinger Equations." Abstr. Appl. Anal. 2013 1 - 7, 2013. https://doi.org/10.1155/2013/590653