On the existence of a global solution of the Cauchy problem for a Klein- Gordon-Dirac system (Q1113375)

We prove the existence of a unique global solution of the Cauchy problem for the Klein-Gordon-Dirac system \[ i(\partial \psi /\partial t)=- i\alpha \cdot \nabla \psi +(M-k\phi)\beta \psi;\quad \partial^ 2\phi /\partial t^ 2=\Delta \phi -m^ 2\phi +k\psi +\beta \psi, \] where \(M\geq 0\), \(m>0\) and \(k=k(r)\), \(r=| x|\), \(x\in {\mathbb{R}}^ 3\), such that \(k\in C^ 1({\mathbb{R}}_+;{\mathbb{R}})\), \(k/r\in W^{1,\infty}({\mathbb{R}}_+)\), for initial data with certain symmetries but not necessarily ``small''.