# Unconditional uniqueness in the charge class for the Dirac-Klein-Gordon equations in two space dimensions

Recently, A. Gruenrock and H. 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 $H^{s+1-2} \times H^{s-1-2}$, respectively, where $s\ge 0$, but uniqueness was only known in a contraction space of Bourgain type, strictly smaller than the natural solution space $C0,T; H^s \times H^{s+1-2} \times H^{s-1-2}$. Here we prove uniqueness in the latter space for $s \ge 0$. This improves a recent result of H. Pecher, where the range $s1-30$ was covered.

Author: Sigmund Selberg; Achenef Tesfahun

Source: https://archive.org/