Relaxation-time limits of non-isentropic hydrodynamic models for semiconductors

This work deals with non-isentropic hydrodynamic models for semiconductors with short momentum and energy relaxation-times. The high- and low-frequency decomposition methods are used to construct uniform (global) classical solutions to Cauchy problems of a scaled hydrodynamic model in the framework of critical Besov spaces. Furthermore, it is rigorously justified that the classical solutions strongly converge to that of a drift-diffusion model, as two relaxation times both tend to zero. As a by-product, global existence of weak solutions to the drift-diffusion model is also obtained