TY - JOUR
T1 - Existence and Approximation of Statistical Solutions of the 3D MHD Equations
AU - Zhang , Yuanyuan
AU - Chen , Guanggan
JO - Journal of Partial Differential Equations
VL - 3
SP - 326
EP - 354
PY - 2024
DA - 2024/08
SN - 37
DO - http://doi.org/10.4208/jpde.v37.n3.7
UR - https://global-sci.org/intro/article_detail/jpde/23346.html
KW - 3D MHD equations, Vishik-Fursikov measures, stationary statistical solutions, convergence of measures.
AB - <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>