Local well-posedness of the two-dimensional Dirac–Klein–Gordon equations in Fourier–Lebesgue spaces

Abstract

The local well-posedness problem is considered for the Dirac–Klein–Gordon system in two space dimensions for data in Fourier–Lebesgue spaces [Formula: see text], where [Formula: see text] and [Formula: see text] and [Formula: see text] denote dual exponents. We lower the regularity assumptions on the data with respect to scaling improving the results of d’Ancona et al. in the classical case [Formula: see text]. Crucial is the fact that the nonlinearities fulfill a null condition as detected by these authors.