Global Existence of Solutions to the Cauchy Problem for the Relativistic Vlasov–Maxwell–Fokker–Planck System in Low-Regularity Spaces

This paper establishes the global-in-time existence and uniqueness of mild solutions to the relativistic Vlasov–Maxwell–Fokker–Planck (VMFP) system near a global Maxwellian equilibrium. We adopt a low-regularity functional framework, namely the mixed-norm space Lk1LT∞Lp2 introduced for kinetic equations, which requires only integrability in the Fourier frequency variable and avoids high-order spatial differentiability. By employing a macro–micro decomposition, we derive macroscopic estimates for the hydrodynamic density and electric field, complemented by coercive estimates for the microscopic dissipation. Under a smallness assumption on the initial perturbation measured in this low-regularity norm, we derive a uniform a priori bound for the associated energy functional. This work provides the global existence result for the relativistic VMFP system in such low-regularity spaces, significantly relaxing the regularity requirements of previous classical Sobolev approaches.