Communications in Mathematical Sciences

Volume 19 (2021)

Number 8

Time-periodic solution for an incompressible magnetohydrodynamic system with an external force in $\mathbb{R}^N$

Pages: 2081 – 2118



Yitong Pei (Department of Mathematics, Nanjing University of Science and Technology, Nanjing, China; and Graduate School of China Academy of Engineering Physics, Beijing, China)

Boling Guo (Institute of Applied Physics and Computational Mathematics, Beijing, China)


In this paper, we study the existence and uniqueness of time-periodic solutions to incompressible magnetohydrodynamic equations. Our approach combines energy estimates with topological degree theory, and our result follows from a limiting process. The main difficulty is to prove the compactness and continuity for a key operator $\Lambda$ given in Definition 2.1, the proof is based on parabolic regularization.


incompressible magnetohydrodynamic equations, time-periodic solutions, topological degree theory

2010 Mathematics Subject Classification

35L70, 35Q35, 35Q55, 76B15

Received 27 May 2020

Accepted 20 April 2021

Published 7 October 2021