Local Propagation of Momentum Moments for the Relativistic Vlasov--Poisson System

This paper proves local propagation of momentum moments of order $k\ge 5\mathrm{/}2$ for the three-dimensional relativistic Vlasov–Poisson system. In the Coulomb case, this improves the previous result which requires integer moments of order $k\ge 3$. The proof adapts the critical density method developed in our recent work on the classical Vlasov–Poisson equation. We introduce a weighted kinetic tensor adapted to the relativistic velocity and obtain the critical density estimate. This estimate then allows us to close the moment argument by a short-time bootstrap.