Time periodic solutions for the non-isentropic compressible quantum hydrodynamic equations with viscosity in R^3
DOI:
https://doi.org/10.58997/ejde.2020.103Keywords:
Time periodic solutions; uniform energy estimates; full quantum hydrodynamic equations with viscosity; Leray-Schauder degree theory.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
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