A Remark on Unconditional Uniqueness in the Chern-Simons-Higgs Model
Selberg, Sigmund · da Silva, Daniel Oliveira
الأصل · EN
The solution of the Chern-Simons-Higgs model in Lorenz gauge with data for the potential in Hˢ⁻¹/² and for the Higgs field in Hˢ × Hˢ⁻¹ is shown to be unique in the natural space C([0,T];Hˢ⁻¹/² × Hˢ × Hˢ⁻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 Yˢ of Bourgain type. We prove that any solution in C([0,T];H¹/² × H¹ × L²) must in fact belong to the space Y³/⁴⁺ε, hence it is the unique solution obtained by Huh and Oh.
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