Global well-posedness of the Chern-Simons-Higgs equations with finite energy

2012/01/04 by Selberg, Sigmund, Tesfahun, Achenef
#35L70 #35Q40 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1201.0975

Abstract

We prove that the Cauchy problem for the Chern-Simons-Higgs equations on the (2+1)-dimensional Minkowski space-time is globally well posed for initial data with finite energy. This improves a result of Chae and Choe, who proved global well-posedness for more regular data. Moreover, we prove local well-posedness even below the energy regularity, using the the null structure of the system in Lorenz gauge and bilinear space-time estimates for wave-Sobolev norms.

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