报告人：孙文龙 副教授

时 间：2024-10-24 14:30:00

地 点：理科楼L2620

报告摘要：A viscous quantum hydrodynamic system for particle density, current density, energy density and electrostatic potential, coupled with a Poisson equation, is studied in spatial one dimensional real line. The system is self-consistent in the sense that the electric field, which forms a forcing term in the momentum and energy equations, is determined by the coupled Poisson equation. First the existence and uniqueness of the stationary solution is proved in an appropriate Sobolev space. Then exponential stability of the stationary solution is established by constructing an apriori estimate. Since the techniques for classical hydrodynamic equations are not applicable here due to the quantum term, the existence of a local-in-time solution is obtained by showing the existence of local-in-time solutions of a reformulated system via the iteration method.