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

TL;DR

This paper proves unconditional uniqueness for the 2D Dirac-Klein-Gordon equations in the natural energy space, extending previous results and covering the full charge class for initial data with regularity s ≥ 0.

Contribution

It establishes unconditional uniqueness in the natural solution space for all s ≥ 0, improving prior work limited to s > 1/30.

Findings

Unconditional uniqueness holds in the natural solution space for s ≥ 0.

Extends the range of s from > 1/30 to all s ≥ 0.

Improves understanding of well-posedness for the 2D Dirac-Klein-Gordon system.

Abstract

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 $C([0,T]; H^s \times H^{s+1/2} \times H^{s-1/2})$. Here we prove uniqueness in the latter space for $s \ge 0$. This improves a recent result of H. Pecher, where the range $s>1/30$ was covered.