Vlasov-Poisson-Landau (Fokker-Planck) 方程解的大时间行为

In this paper, we consider the initial value problems for Vlasov-Poisson-Fokker-Planck (VPFP) equations and Vlasov-Poisson-Landau (VPL) equations. We give the spectrum analysis and semigroup estimates on the linearized VPFP equations and VPL equations around their equilibrium states and show the optimal convergence rates of global solution to nonlinear problems. We show that the solution to VPFP equations tends to the equilibrium state at the exponential convergence rate, the solution to VPL equations tends to the equilibrium state at the algebraic convergence rate (1+t)^−1/4 when initial values are small perturbations of global Maxwellian.