GLOBAL CLASSICAL SOLUTIONS FOR THE VLASOV-NORDSTRÖM-FOKKER-PLANCK SYSTEM

In this paper we consider the Vlasov-Nordström-Fokker-Planck system in the whole space. The kinetic model is a relativistic generalization of the classical Vlasov-Poisson-Fokker-Planck system in the gravitational case and describes the ensemble motion of collision particles interacting by means of a self-consistent scalar gravitational field satisfying a nonlinear wave equation. We construct the global-in-time classical solutions to the corresponding Cauchy problem with small perturbation of equilibrium states, and we further obtain the polynomial rate of convergence of solutions to the Maxwell-Jüttner distribution function with a constant scalar gravitational field. The proof is based on the dissipative structure analysis of the linearized system together with the nonlinear energy method. In particular, we make use of the Klein-Gordon dissipation feature induced by the coupling and also overcome difficulties due to degenerate dissipation of momentum derivatives.