QUANTUM EULER-POISSON SYSTEM: LOCAL EXISTENCE OF SOLUTIONS

摘要

The one-dimensional transient quantum Euler-Poisson system for semiconductors is studied in a bounded interval.The quantum correction can be interpreted as a dispersive regularization of the classical hydrodynamic equations and mechanical effects.The existence and uniqueness of local-in-time solutions are proved with lower regularity and without the restriction on the smallness of velocity,where the pressure-density is general (can be non-convex or non-monotone).