Hsiao, Ling et al., Convergence of the Vlasov.Poisson.Boltzmann System to the Incompressible Euler Equations, Acta mathematica Sinica. English series (Print) , 23(4), 2007, pp. 761-768
In this paper we establish the convergence of the Vlasov.Poisson.Boltzmann system to the incompressible Euler equations in the so.called quasi.neutral regime. The convergence is rigorously proved for time intervals on which the smooth solution of the Euler equations of the incompressible fluid exists. The proof relies on the relative.entropy method.