A Remark on Unconditional Uniqueness in the Chern-Simons-Higgs Model

2013/10/13 by Sigmund Selberg, Daniel Oliveira da Silva, Selberg, Sigmund +1
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.1310.3503

arxiv created 2013/10/13 · arxiv updated 2013/10/15

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 × H^s-1 is shown to be unique in the natural space C([0,T];H^s-1/2 × H^s × H^s-1) for s ≥ 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 × H¹ × L²) must in fact belong to the space Y^3/4+ε, hence it is the unique solution obtained by Huh and Oh.

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