A REMARK ON UNCONDITIONAL UNIQUENESS IN THE CHERN-SIMONS-HIGGS MODEL

作者：Selberg Sigmund^*; da Silva Daniel Oliveira

来源：Differential and Integral Equations, 2015, 28(3-4): 333-346.

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 H-s x Hs-1 is shown to be unique in the natural space C([0, T]; Hs-1/2 x H-s x 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 Upsilon(s) of Bourgain type. We prove that any solution in C([0,T]; H-1/2 x H-1 x L-2) must in fact belong to the space Upsilon(3/4+epsilon). Hence, it is the unique solution obtained by Huh and Oh.

• 出版日期2015-4