Small data scattering of Dirac equations with Yukawa type potentials in $L_x^2(\mathbb R^2)$

Abstract

We revisit the Cauchy problem of nonlinear massive Dirac equation with Yukawa type potentials F [ (b + |ξ|) ] in 2 dimensions. The authors of [10, 4] obtained small data scattering and large data global well-posedness in H for s > 0, respectively. In this paper we show that the small data scattering occurs in L x (R). This can be done by combining bilinear estimates and modulation estimates of [12, 10].