Existence and asymptotic analysis of a Vlasov–Fokker–Planck/Magnetohydrodynamic system

In this paper, we study the global existence of weak solutions and asymptotic analysis of the coupled system of the Vlasov–Fokker–Planck (VFP) equation and magnetohydrodynamic (MHD) equations, where two systems are coupled via drag force. In particular, we consider the case when the velocity of the particle is also relaxed to the locally averaged velocity. The global existence of a weak solution is guaranteed by regularizing the original system and then deriving an appropriate compactness of the regularized solution. Moreover, we consider the regime where the local-alignment and diffusion force are strong, so that the solution to the VFP/MHD system converges to the Euler/MHD system, as the singular parameter tends to 0. To attain a rigorous convergence analysis, we rely on the celebrated relative entropy method.