We study the uniqueness and regularity of Leray-Hopf's weak solutions for the MHD equations with dissipation and resistance in different frameworks. Using different kinds of space-time estimates in conjunction with the Littlewood-Paley-Bony decomposition, we present some general criteria of uniqueness and regularity of weak solutions to the MHD system, and prove the uniqueness and regularity criterion in the framework of mixed space-time Besov spaces by applying Tao's trichotomy method.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc74-0-4,
author = {Marco Cannone and Changxing Miao and Nicolas Prioux and Baoquan Yuan},
title = {The Cauchy problem for the magneto-hydrodynamic system},
journal = {Banach Center Publications},
volume = {72},
year = {2006},
pages = {59-93},
zbl = {1104.76085},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc74-0-4}
}
Marco Cannone; Changxing Miao; Nicolas Prioux; Baoquan Yuan. The Cauchy problem for the magneto-hydrodynamic system. Banach Center Publications, Tome 72 (2006) pp. 59-93. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc74-0-4/