Remarks on regularity and uniqueness of the Dirac–Klein–Gordon equations in one space dimension

Abstract

In recent work, the authors extended the local and global well-posedness theory for the 1D Dirac–Klein–Gordon equations, but the uniqueness of the solutions was only known in the contraction spaces (of Bourgain–Klainerman–Machedon type). Here we prove some unconditional uniqueness results [that is, uniqueness in the larger space C([0,T];X0), where X0 denotes the data space]. We also prove a result about persistence of higher regularity, which is stronger than the standard version obtained from the contraction argument, since our result allows to independently increase the regularity of the spinor and scalar fields, whereas in the standard result they must be increased by the same amount.