LAUSR

In this paper, we establish the existence and uniqueness of a time‐periodic solution to the full compressible quantum Euler equations. First, we prove the existence of time‐periodic solutions under some smallness assumptions imposed on the external force in a periodic domain by a regularized approximation scheme and the Leray–Schauder degree theory. Then the result is generalized to ℝ3 by adapting a limiting method and a diagonal argument. The uniqueness of the time‐periodic solutions is also given. Compared to classical Euler equations, the third‐order quantum spatial derivatives are considered which need some elaborated treatments thereof in obtaining the highest‐order energy estimates.