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 \(\mathbb{R}^3\). 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 \(\epsilon\)) estimates, especially in the selection of the norm.
For more information see https://ejde.math.txstate.edu/Volumes/2020/103/abstr.html