Energy Solution to the Chern-Simons-Schrödinger Equations

Hyungjin Huh

doi:10.1155/2013/590653

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Home > Journals > Abstr. Appl. Anal. > Volume 2013 > Article

2013 Energy Solution to the Chern-Simons-Schrödinger Equations

Hyungjin Huh

Abstr. Appl. Anal. 2013: 1-7 (2013). DOI: 10.1155/2013/590653

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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.