Year: 2024
Author: Yuanyuan Zhang, Guanggan Chen
Journal of Partial Differential Equations, Vol. 37 (2024), Iss. 3 : pp. 326–354
Abstract
This paper focuses on the statistical characteristics of the 3D MHD equations. We firstly establish an existence theorem of a Vishik-Fursikov measure of the 3D MHD equations by taking advantage of the Krein-Milman theorem along with some functional and measure theories. Then by applying the Topsoe lemma on the constructed trajectory space possessing some special topological properties, we show that the Vishik-Fursikov measure and the stationary Vishik-Fursikov statistical solution of the 3D MHD system are approximated by the counterparts of the 3D MHD-$α$ system, respectively, as the parameter $α$ decreases to zero.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jpde.v37.n3.7
Journal of Partial Differential Equations, Vol. 37 (2024), Iss. 3 : pp. 326–354
Published online: 2024-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 29
Keywords: 3D MHD equations Vishik-Fursikov measures stationary statistical solutions convergence of measures.