Global existence and large time behavior of classical solutions to the Euler-Maxwell-Vlasov-Fokker-Planck system

Abstract

We consider global classical solutions to the Cauchy problem for an Euler-Maxwell-Vlasov-Fokker-Planck system, which is a fluid-particle model describe the evolutions of disperse two-phase flows. In these two-phase flows, the compressible Euler-Maxwell equations modeling a dense phase (fluid) and the Vlasov-Fokker-Planck equation for the dispersed phase (particles) which is usually considered from the statistical view of point. They are coupled through the friction force. Global existence of classical solutions to the Cauchy problem in R3 is established when initial data is a small perturbation of some given equilibrium. The algebraic rate of convergence of solution toward the equilibrium state is also obtained under additional conditions on initial data. The proof is based on the classical energy estimates and Fourier multiplier technique, which are considerably complicated and some new ideas and techniques are thus required.