Low regularity global solutions of the Dirac-Klein-Gordon equations in one space dimension

Abstract

We prove global existence for the Dirac-Klein-Gordon equations in one space dimension with $\psi\in L^2$ (charge class) and $\phi\in H^{1/4}$. This improves the global existence result of Fang [7] by $1/4 + \epsilon$ derivatives in $\phi$. The proof relies on bilinear estimates for solutions of the Dirac equation and a decomposition of the spinor field into `left' and `right' spinors.