Abstract and Applied Analysis
Volume 2013 (2013), Article ID 590653, 7 pages
http://dx.doi.org/10.1155/2013/590653
Research Article

Energy Solution to the Chern-Simons-Schrödinger Equations

Hyungjin Huh

Department of Mathematics, Chung-Ang University, Seoul 156-756, Republic of Korea

Received 19 November 2012; Accepted 17 January 2013

Academic Editor: Graziano Crasta

Copyright © 2013 Hyungjin Huh. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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 . 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.