Asymptotics toward rarefaction wave for the inflow problem of the two-fluid quantum Navier–Stokes–Poisson system
摘要
This paper studies the large-time behavior of solutions to the inflow problem of the 1-D two-fluid quantum Navier–Stokes–Poisson system, which describes the transport of electrons and holes in ultra-small nanoscale semiconductors. Based on a refined energy method by taking into account both the effect of the quantum Bohm potentials and the electrostatic potential, we establish the asymptotic stability of the rarefaction wave for this inflow problem in the case that the initial perturbation is sufficiently small. To the best of our knowledge, such a result is the first rigorous result for the inflow problem of the two-fluid quantum Navier–Stokes–Poisson system.