Energy Solution to the Chern-Simons-Schrödinger Equations

الملخص EN

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 H1(ℝ2).

The Coulomb gauge provides elliptic features for gauge fields A0,Aj.

The Koch- and Tzvetkov-type Strichartz estimate is applied with Hardy-Littlewood-Sobolev and Wente's inequalities.