Differential and Integral Equations

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

Sigmund Selberg and Daniel Oliveira da Silva

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

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

Permanent link to this document
https://projecteuclid.org/euclid.die/1423055231

Mathematical Reviews number (MathSciNet)
MR3306566

Zentralblatt MATH identifier
1363.35300

Subjects
Primary: 35Q40: PDEs in connection with quantum mechanics 35L70: Nonlinear second-order hyperbolic equations 81V10: Electromagnetic interaction; quantum electrodynamics

Citation

Selberg, Sigmund; da Silva, Daniel Oliveira. A remark on unconditional uniqueness in the Chern-Simons-Higgs model. Differential Integral Equations 28 (2015), no. 3/4, 333--346. https://projecteuclid.org/euclid.die/1423055231


Export citation