arXiv Analytics

Sign in

arXiv:1912.11353 [math.AP]AbstractReferencesReviewsResources

Almost Optimal Local Well-Posedness of the Chern-Simons-Dirac System in the Coulomb Gauge

Seokchang Hong, Kiyeon Lee

Published 2019-12-23Version 1

In this paper, we consider the Cauchy problem of regularity and uniqueness of the Chern-Simons-Dirac system in the Coulomb gauge for initial data in $B^0_{2,1}$. The novelty of this paper is on proving almost critical regularity by using the full localization of space-time Fourier side and bilinear estimates given by Selberg. We also prove the Dirac spinor flow of Chern-Simons-Dirac system cannot be $C^3$ at the origin in $H^s$ if $s<0$.

Comments: 23 pages. arXiv admin note: text overlap with arXiv:1912.06790
Categories: math.AP
Related articles: Most relevant | Search more
arXiv:1110.6345 [math.AP] (Published 2011-10-28)
Local and global well-posedness for the Chern-Simons-Dirac system in one dimension
arXiv:1912.06790 [math.AP] (Published 2019-12-14)
Well-posedness in a critical space of Chern-Simons-Dirac system in the Lorenz gauge
arXiv:math/0101120 [math.AP] (Published 2001-01-13, updated 2002-02-20)
Almost optimal local well-posedness of the Maxwell-Klein-Gordon equations in 1+4 dimensions

Links

Toolbox