The 3D relativistic Vlasov-Maxwell system is one of the fundamental models in the plasma physics, which describes the dynamics of electrons and ions under the electromagnetic field created by particles themselves. A major open problem in the field is the existence of global solution for smooth localized large initial data. 

Inspired by the smoothing effect identified by Klainerman-Staffilani in 2002, we reveal a new iterative smoothing scheme together with a new weighted space-time estimate of the distribution function for the axisymmetric case. As a result, we are able to control the velocity characteristics over time via a bootstrap argument, which provide further control for the $L^\infty_x$-norm of the electromagnetic field over time by using the classic moment method. It confirms the continuation criteria of Luk-Strain (2014), which means that the regular solution doesn’t blow up in finite time, i.e., solution is indeed global.