Resumen
This work is concerned with multidimensional isentropic hydrodynamical models for semiconductors with short momentum relaxation time. With the help of the Maxwell iteration, we prove that, as the relaxation time tends to zero, periodic initial-value problems of a certain scaled hydrodynamical model have unique smooth solutions existing in the time interval where the classical drift-diffusion model has smooth solutions. Meanwhile, we justify a formal derivation of the latter from the former.