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March/April 2015 A remark on unconditional uniqueness in the Chern-Simons-Higgs model
Sigmund Selberg, Daniel Oliveira da Silva
Differential Integral Equations 28(3/4): 333-346 (March/April 2015).

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.

Citation

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Sigmund Selberg. Daniel Oliveira da Silva. "A remark on unconditional uniqueness in the Chern-Simons-Higgs model." Differential Integral Equations 28 (3/4) 333 - 346, March/April 2015.

Information

Published: March/April 2015
First available in Project Euclid: 4 February 2015

zbMATH: 1363.35300
MathSciNet: MR3306566

Subjects:
Primary: 35L70, 35Q40, 81V10

Rights: Copyright © 2015 Khayyam Publishing, Inc.

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Vol.28 • No. 3/4 • March/April 2015
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