On the bipolar multidimensional quantum Euler–Poisson system: The thermal equilibrium solution and semiclassical limit

In this paper we establish the existence of a unique thermal equilibrium solution of the bipolar multidimensional quantum Euler–Poisson system over the whole space R3R3 and obtain the relevant semiclassical limit and a combined Planck–Debye length limit through using energy estimating methods and a fixed point theory.