Global classical solutions of the 3D relativistic Vlasov-Maxwell system for large data

Claims that every smooth admissible datum ($f_0\in C_c^\infty$, $f_0\ge0$, fields in $C_b^\infty\cap L^2$ satisfying $\nabla\cdot E_0=\rho_{f_0}$, $\nabla\cdot B_0=0$) generates a unique global classical solution of the one-species relativistic Vlasov-Maxwell system in three dimensions, smooth on every $[0,T]$ with compact phase-space support there. The key estimate controls the signed momentum impulse along characteristics, integrating the retarded force along source trajectories before taking absolute values, which rules out momentum blow-up and lets the Glassey-Strauss criterion apply. It treats one species without background charge; it does not give uniform-in-time momentum bounds (the support may grow with $T$) or asymptotic behaviour, and it does not cover the non-relativistic or multi-species systems explicitly.

Claims that every smooth admissible datum ($f_0\in C_c^\infty$, $f_0\ge0$, fields in $C_b^\infty\cap L^2$ satisfying $\nabla\cdot E_0=\rho_{f_0}$, $\nabla\cdot B_0=0$) generates a unique global classical solution of the one-species relativistic Vlasov-Maxwell system in three dimensions, smooth on every $[0,T]$ with compact phase-space support there. The key estimate controls the signed momentum impulse along characteristics, integrating the retarded force along source trajectories before taking absolute values, which rules out momentum blow-up and lets the Glassey-Strauss criterion apply. It treats one species without background charge; it does not give uniform-in-time momentum bounds (the support may grow with $T$) or asymptotic behaviour, and it does not cover the non-relativistic or multi-species systems explicitly.