Differential and Integral Equations

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

Sigmund Selberg and Daniel Oliveira da Silva

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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

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

First available in Project Euclid: 4 February 2015

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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

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