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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
DOI: https://dx.doi.org/10.4310/CMS.2021.v19.n8.a2
Authors
Abstract
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.
Keywords
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