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We prove low regularity local well-posedness results inBourgain-Klainerman-Machedon spaces for the Chern-Simons-Dirac system in thetemporal gauge and the Coulomb gauge. Under slightly stronger assumptions onthe data we also obtain "unconditional" uniqueness in the natural solutionspaces.

Low regularity solutions for Chern-Simons-Dirac systems in the temporal and Coulomb gauge