On the Cauchy Problem for the Vlasov-Maxwell-Fokker-Planck System in Low Regularity Space

In this study, we investigate the Cauchy problem for the Vlasov-Maxwell-Fokker-Planck system near a global Maxwellian in low regularity space. We establish the existence of global mild solutions to the system by employing the energy method, provided that the perturbative initial data is sufficiently small. Moreover, despite the absence of zeroth-order dissipation for the magnetic field, we are able to derive exponential decay estimates for solutions in higher-order regularity space. This is achieved by leveraging the higher-order dissipation properties of the magnetic field, which are deduced from the Maxwell equation.