CONVERGENCE FROM THE TWO-SPECIES VLASOV-POISSON-BOLTZMANN SYSTEM TO THE TWO-FLUID INCOMPRESSIBLE NAVIER-STOKES-FOURIER-POISSON SYSTEM WITH OHM'S LAW

In this paper,we justify the convergence from the two-species Vlasov-PoissonBoltzmann(VPB,for short)system to the two-fluid incompressible Navier-Stokes-FourierPoisson(NSFP,for short)system with Ohm’s law in the context of classical solutions.We prove the uniform estimates with respect to the Knudsen numberεfor the solutions to the two-species VPB system near equilibrium by treating the strong interspecies interactions.Consequently,we prove the convergence to the two-fluid incompressible NSFP asεgoes to 0.

THE VLASOV-POISSON-BOLTZMANN SYSTEM NEAR MAXWELLIANS FOR LONG-RANGE INTERACTIONS

In this article, we are concerned with the construction of global smooth smallamplitude solutions to the Cauchy problem of the one species Vlasov-Poisson-Boltzmann system near Maxwellians for long-range interactions. Compared with the former result obtained by Duan and Liu in [12] for the two species model, we do not ask the initial perturbation to satisfy the neutral condition and our result covers all physical collision kernels for the full range of intermolecular repulsive potentials.

Convergence of the Vlasov-Poisson-Boltzmann System to the Incompressible Euler Equations

在这篇论文，我们在所谓的伪中立的政体建立 Vlasov-Poisson-Boltzmannsystem 的集中到不可压缩的 Euler 方程。集中严厉地为上的时间间隔被证明茶碱的 Euler 方程的光滑的答案可压缩的液体存在。证明依靠相对熵的方法。