## Abstract and Applied Analysis

### Energy Solution to the Chern-Simons-Schrödinger Equations

Hyungjin Huh

#### Abstract

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 ${H}^{1}\left({ℝ}^{2}\right)$. 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.

#### Article information

Source
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 590653, 7 pages.

Dates
First available in Project Euclid: 27 February 2014

https://projecteuclid.org/euclid.aaa/1393511764

Digital Object Identifier
doi:10.1155/2013/590653

Mathematical Reviews number (MathSciNet)
MR3035224

Zentralblatt MATH identifier
1276.35138

#### Citation

Huh, Hyungjin. Energy Solution to the Chern-Simons-Schrödinger Equations. Abstr. Appl. Anal. 2013 (2013), Article ID 590653, 7 pages. doi:10.1155/2013/590653. https://projecteuclid.org/euclid.aaa/1393511764

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