Relaxation-Time Limit in the Isothermal Hydrodynamic Model for Semiconductors

Abstract

This work is concerned with the relaxation-time limit in the multidimensional isothermal hydrodynamic model for semiconductors in the critical Besov space. As the initial data are sufficiently close to equilibrium, the uniform (global) classical solutions are constructed by the high- and low-frequency decomposition methods. Furthermore, it is shown that the scaled classical solutions strongly converge towards that of a drift-diffusion model, as the relaxation time tends to zero.