In the present paper, we study the diffusion limit of the classical solution to the Vlasov-Poisson-Fokker-Planck (VPFP) system with initial data near a global Maxwellian. We prove the convergence and establish the optimal convergence rate of the global strong solution to the VPFP system towards the solution to the drift-diffusion-Poisson system based on the spectral analysis with precise estimation on the initial layer.
Diffusion Limit with Optimal Convergence Rate of Classical Solutions to the Vlasov-Maxwell-Boltzmann System
Diffusion Limit of the Vlasov-Poisson-Boltzmann System
Global strong solutions to 3-D Navier-Stokes system with strong dissipation in one direction
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