## Differential and Integral Equations

### A remark on unconditional uniqueness in the Chern-Simons-Higgs model

#### Abstract

The solution of the Chern-Simons-Higgs model in Lorenz gauge with data for the potential in $H^{s-1/2}$ and for the Higgs field in $H^s \times H^{s-1}$ is shown to be unique in the natural space $C([0,T];H^{s-1/2} \times H^s \times H^{s-1})$ for $s \ge 1$, where $s=1$ corresponds to finite energy. Huh and Oh recently proved local well-posedness for $s > 3/4$, but uniqueness was obtained only in a proper subspace $Y^s$ of Bourgain type. We prove that any solution in $C([0,T];H^{1/2} \times H^1 \times L^2)$ must in fact belong to the space $Y^{3/4+\epsilon}$. Hence, it is the unique solution obtained by Huh and Oh.

#### Article information

Source
Differential Integral Equations, Volume 28, Number 3/4 (2015), 333-346.

Dates
First available in Project Euclid: 4 February 2015