Time periodic solutions for the non-isentropic compressible quantum hydrodynamic equations with viscosity in R^3

Abstract

This article concerns the existence and uniqueness of a time periodic solution for the non-isentropic quantum hydrodynamic equations with viscosity. By applying the Leray-Schauder theory, subtle energy estimates and a limiting method, we obtain the existence of time periodic solutions under some smallness assumptions on the time periodic external force in ℝ3. The uniqueness can be proved by similar energy estimates. In particular, the quantum effects and the energy equation are taken into account in this paper which play a significant role in the uniform (in the domain R and the positive constant ε) estimates, especially in the selection of the norm.