Global charge class solutions of the Dirac-Klein-Gordon equations in one space dimension

Abstract

In a recent paper [3] we proved global well posedness for the Dirac-Klein-Gordon equations with Yukawa interaction in $1+1$ dimensions with initial data $\psi_{0}\in L^2(\mathbb R) $, $(\phi_{0},\phi_{1})\in {H^{r}(\mathbb R)} \times {H^{r-1}(\mathbb R)} $, where $r\in[1/4,1]$, $r\neq 1/2$. In this paper we use a new null form estimate to prove global well posedness for the more difficult case $r=1/2$.