Electronic Journal of Differential Equations,
Vol. 2009(2009), No. 114, pp. 1-10.

Title: Low regularity solutions of the Chern-Simons-Higgs equations
       in the Lorentz gauge

Author: Nikolaos Bournaveas (Univ. of Edinburgh, UK)

Abstract:
 We prove local well-posedness for the 2+1-dimensional
 Chern-Simons-Higgs equations in the Lorentz gauge with initial
 data of low regularity. Our result improves earlier results
 by Huh [10, 11].

Submitted February 22, 2009. Published September 12, 2009.
Math Subject Classifications: 35L15, 35L70, 35Q40.
Key Words: Chern-Simons-Higgs equations; Lorentz gauge;
           null-form estimates; low regularity solutions.