@Article{JPDE-37-326,
author = {Zhang , Yuanyuan and Chen , Guanggan},
title = {Existence and Approximation of Statistical Solutions of the 3D MHD Equations},
journal = {Journal of Partial Differential Equations},
year = {2024},
volume = {37},
number = {3},
pages = {326--354},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2079-732X},
doi = {https://doi.org/10.4208/jpde.v37.n3.7},
url = {http://global-sci.org/intro/article_detail/jpde/23346.html}
}