Existence of global solutions to nonlinear massless Dirac system and wave equation with small data (Q1818032)

This paper deals with the Cauchy problem for a semilinear massless Dirac system. The author proves the existence of a global solution assuming the initial data to be sufficiently small. The approach here used is based on the conservation law of charge and on Sobolev type weighted estimates for the spinor field. Similar methods enable the author to prove global existence for the Cauchy problem for the wave equation, with nonlinearity in the right-hand side \(|u_t|^\nu\), \(\nu> 2\) in 3 space dimensions. This way he generalizes some results of T. Sideris and H. Takamura where the case of spherically symmetric initial data was considered only.