We prove the large time existence of solutions to the magnetohydrodynamics equations with slip boundary conditions in a cylindrical domain. Assuming smallness of the L₂-norms of the derivatives of the initial velocity and of the magnetic field with respect to the variable along the axis of the cylinder, we are able to obtain an estimate for the velocity and the magnetic field in without restriction on their magnitude. Then the existence follows from the Leray-Schauder fixed point theorem.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am38-2-1,
author = {Wisam Alame and Wojciech M. Zaj\k aczkowski},
title = {Large time regular solutions to the MHD equations in cylindrical domains},
journal = {Applicationes Mathematicae},
volume = {38},
year = {2011},
pages = {117-146},
zbl = {1215.35125},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am38-2-1}
}
Wisam Alame; Wojciech M. Zajączkowski. Large time regular solutions to the MHD equations in cylindrical domains. Applicationes Mathematicae, Tome 38 (2011) pp. 117-146. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am38-2-1/