Global existence for the quadratic Dirac equation in two and three space dimensions

In this paper we study global existence and pointwise decay estimates for the nonlinear Dirac equation with quadratic nonlinearity. We consider four cases depending on the spatial dimension n, the mass parameter m, and the initial data.0: i)(n, m) =(2, 0) and psi(0) is compactly supported; ii)(n, m) =(3, 0) and psi(0) is compactly supported; iii)(n, m) =(3, 0) and.0is not necessarily compactly supported; iv) n = 3, m >= 0 and psi(0) is compactly supported. In each of the cases i)-iii), we prove a small data global existence result, a sharp pointwise decay estimate and a scattering result for the global solution. In the case iv) we prove a uniform (in the mass parameter m) global existence result, a unified pointwise decay estimate, and a scattering result. (c) 2022 Elsevier Inc. All rights reserved.