## Energy solution to the Chern-Simons-Schrödinger equations.(English)Zbl 1276.35138

Summary: 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 $$H^1(\mathbb R^2)$$. The Coulomb gauge provides elliptic features for gauge fields $$A_0, A_j$$. The Koch- and Tzvetkov-type Strichartz estimate is applied with Hardy-Littlewood-Sobolev and Wente’s inequalities.

### MSC:

 35Q60 PDEs in connection with optics and electromagnetic theory 35Q40 PDEs in connection with quantum mechanics
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### References:

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