Time periodic solutions for the full quantum Euler equation
• Min LI,
• Xianzhong Yao
Min LI
Shanxi University of Finance and Economics
Author Profile
Xianzhong Yao
Shanxi University of Finance and Economics
Author Profile

## Abstract

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 $\mathbb{R}^{3}$ 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.

#### Peer review status:ACCEPTED

03 Aug 2020Submitted to Mathematical Methods in the Applied Sciences
04 Aug 2020Assigned to Editor
04 Aug 2020Submission Checks Completed
26 Sep 2020Reviewer(s) Assigned
16 Apr 2021Review(s) Completed, Editorial Evaluation Pending
29 May 2021Editorial Decision: Accept