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 ${\mathcal{F}}^{-1}\left[(b^2+|\xi {|}^2{)}^{-1}\right]$ in 2 dimensions. The authors of \cite{tes2d, geosha} obtained small data scattering and large data global well-posedness in $H^s$ for $s>0$, respectively. In this paper we show that the small data scattering occurs in $L_x^2({\mathbb{R}}^2)$. This can be done by combining bilinear estimates and modulation estimates of \cite{yang, tes2d}.

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