Global well-posedness in energy space for the Chern-Simons-Higgs system in temporal gauge

TL;DR

This paper proves global well-posedness of the Chern-Simons-Higgs system in energy space in (2+1) dimensions, improving previous results by employing advanced bilinear estimates and null condition techniques.

Contribution

It establishes the first global well-posedness result in energy space for the system in the temporal gauge, utilizing novel bilinear space-time estimates and null condition analysis.

Findings

Global well-posedness in energy space achieved

Improved upon previous results by Huh

Utilized bilinear estimates and null condition techniques

Abstract

The Cauchy problem for the Chern-Simons-Higgs system in the (2+1)-dimensional Minkowski space in temporal gauge is globally well-posed in energy space improving a result of Huh. The proof uses the bilinear space-time estimates in wave-Sobolev spaces by d'Ancona, Foschi and Selberg, an $L^6_x L^2_t$-estimate for solutions of the wave equation, and also takes advantage of a null condition.