Propagation of Regularity and Long Time Behavior of 3D Massive Relativistic Transport Equation I: Vlasov–Nordström System

In this paper, we introduce a new set of vector fields for the relativistic transport equation, which is applicable general Vlasov-wave type coupled systems. By combining strength Klainerman field method and Fourier method, prove global regularity scattering 3D massive Vlasov–Nordström system small initial data without any compact support assumption, widely used in literature study Vlasov equation.