Abstract
Recently, Grünrock and Pecher proved global well-posedness of the 2d Dirac–Klein–Gordon equations given initial data for the spinor and scalar fields in H s and H s+1/2 × H s-1/2, respectively, where s ≥ 0, but uniqueness was only known in a contraction space of Bourgain type, strictly smaller than the natural solution space C([0,T]; H s × H s+1/2 × H s-1/2). Here we prove uniqueness in the latter space for s ≥ 0. This improves a recent result of Pecher, where the range s > 1/30 was covered.
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Selberg, S., Tesfahun, A. Unconditional uniqueness in the charge class for the Dirac–Klein–Gordon equations in two space dimensions. Nonlinear Differ. Equ. Appl. 20, 1055–1063 (2013). https://doi.org/10.1007/s00030-012-0196-8
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DOI: https://doi.org/10.1007/s00030-012-0196-8